Main Semiconductor Device Measurements

Semiconductor Device Measurements

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In the 60's and 70's, Tektronix was known for the superb precision and high-frequency circuit design. To learn about circuit design, students of engineering would study the designs coming out of Tektronix for clues about how to achieve such remarkable performance. I recall using a Tektronics 7904 1GHz analog 'scope in the 80's and just being astonished by the clarity and precision of the displays.

The Tektronix engineers wrote a series of texts about the problem of measurement in general, and how to design the circuits to reveal the secrets of the domains being measures.

Manuals issued during this most productive time, even today's engineers can learn a great deal by studying the designs in these books.
Year:
1969
Publisher:
Tektronix
Language:
english
Pages:
171
Series:
Measurement Concepts
File:
PDF, 39.14 MB
Download (pdf, 39.14 MB)

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Measurement Concepts

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Semiconductor Devices

SEM ICON DUCTOR
DEVICE
MEASUREMENTS
BY

JOHN MULVEY

Significant Contributions
by
JOHN TOMLIN
LEE MILES
ED SMITH

MEASUREMENT CONCEPTS

FIRST EDITION, THIRD PRINTING, NOVEMBER 1969
062-1009-00
PRICE $1.00

© TEKTRONIX, INC.; 1968
BEAVERTON, OREGON 97005
ALL RIGHTS RESERVED

CONTENTS

PREFACE
1

BIPOLAR TRANSISTORS

1

FORWARD CURRENT TRANSFER

1

h FE , hFE(INV), h fe , h fb , h fc
SATURATION VOLTAGE AND CURRENT

24

VCE(sat) , rCE(sat)
CUTOFF CURRENT AND VOLTAGE BREAKDOWN

28

I CBO
ICEO
ICER
ICEX

and V(BR)CBO' IEBO and V(BR)EBO'
and V(BR)CEO' ICES and V(BR)CES'
and V(BR)CER, I CEV and V(BR)CEV,
and V(BR)CEX, collector sustaining
voltage, avalanche breakdown, punch
through and reach through

SWITCHING TIME

43

turn-on and turn-off time, delay time,
risetime, carrier storage time, fall time
INPUT CAPACITANCE

53

OUTPUT CAPACITANCE

54

HIGH-FREQUENCY CURRENT GAIN

54

fhfe> fT> fhfb

INPUT IMPEDANCE

56

hIE and hie' h IB and h ib
h IC and h ic ' emitter followers
OUTPUT ADMITTANCE

62

REVERSE VOLTAGE TRANSFER

67

continued ...

2

71

FIELD EFFECT TRANSISTORS
LEAKAGE AND BREAKDOWN

71

I GSS

and V(BR)GSS
drain breakdown

FORWARD TRANSFER

79

I DSS ' Vp or VDS(off), Gm
3

UNIJUNCTION TRANSISTORS

4

THYRISTORS (SCRf s ) AND OTHER PNPN DEVICES

89

FORWARD AND REVERSE BLOCKING VOLTAGE

5

SIGNAL DIODES AND RECTIFYING DIODES
99

REVERSE VOLTAGE AND CURRENT

105

REVERSE RECOVERY TIME
STORED CHARGE

106

116

RECTIFICATION EFFICIENCY
JUNCTION CAPACITANCE

117
117

FORWARD RECOVERY TIME

6

ZENER DIODES
Vz

7

117

119

119

ZZK

123

ZZT

123

TUNNEL DIODES AND BACK DIODES

125

PEAK-POINT CURRENT AND VOLTAGE
VALLEY-POINT CURRENT AND VOLTAGE
DIFFERENTIAL RESISTANCE
NEGATIVE RESISTANCE

DEFINITIONS OF TERMS
DEFINITIONS OF SYMBOLS
INDEX

93
99

FORWARD VOLTAGE AND CURRENT

155

133
134

135
147

93

133
133

PREFACE

The concepts for the measurement of semiconductor
characteristics that are covered in this book; 
are embodied by instruments and methods widely used
today. The purpose of the book is not to expose new
ideas, although we certainly hope some will be new
to the average reader.
Instead, its purpose is to
corral what we believe to be many of the better
ideas already in use, and discuss them, particularly
ideas that involve the use of Tektronix instruments.
The reasons for measuring the characteristics of
semiconductor devices fall into about four categories.
Either the measurement is for the purpose of producing
better components, sorting components, predicting
performance in a circuit, or improving a circuit.
The characteristics of semiconductor devices that
are of practical importance to their use in an
electrical circuit can usually be measured with an
electrical instrument. Many of those measurements
also provide good analytical information for people
improving component design or maintaining production
quality and specifications.
Much of the discussion relates to measurements
actually performed, using specific semiconductor types
and instrument types.
These will exemplify a variety
of measurement considerations and concepts. Only
measurements on discrete semiconductor components
are discussed.
Integrated circuits are not covered.
We hope the book may help engineers and technicians
make more meaningful and accurate tests and
measurements of the characteristics of diodes,
transistors, and other semiconductor devices.

1

BIPOLAR TRANSISTORS

Bipolar transistors are those transistors which
normally use current carriers of both polarities.
The category consists mainly of the familiar threeterminal two-junction, NPN or PNP types made of
either germanium or silicon.
FORWARD CURRENT TRANSFER

hFE -- Static Forward Current Transfer Ratio
(Common Emi tter)
hFE

DC beta
DC current
gain

col I ector
current
or base

The static forward current transfer ratio, h FE , of a
transistor, otherwise known as DC beta or DC current
gain is simply the ratio of its collector current
to its base current, assuming, of course, that the
polarity and magnitude of the applied currents and
voltages are within what could be called a correct,
normal operating range for the transistor. The
current gain of any particular transistor is apt
to vary considerably, depending on where within its
normal operating range the transistor is operating.
Therefore, to be more specific when we refer to the
static forward-current transfer ratio of a transistor,
we should say what the collector voltage is supposed
to be, and what either the base current or collector
current is supposed to be. Usually the collector
current is specified, so the base current must be
varied until the specified collector current flows.

current

Sometimes the base current may be sp cified.

specified

case the resultant collector current is then measured.

In that

2

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CURRENT
STEPS

B

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Fig. 1-1.

hFE , 2N3904

SO-~A

base-current step.

3

power
dissipation
may limit
measurements

continuallypulsed mode
for DC beta

DC beta
at any
point

The measurement of base current, collector current,
and collector voltage may be done with DC meters to
determine DC beta. This method soon runs into a
problem when the power dissipated is enough to dominate
the temperature of the transistor. It may even cause
the transistor to be burned out before the test is
completed. It is fundamental that any test or
measurement performed on a semiconductor should not
alter its characteristics. Care should always be
taken to avoid applying excessive currents or
voltages, or both, or the characteristics may be
altered. Interrupting the applied currents and
voltages frequently may be required to keep the
internal temperature down, close to that of the
desired surrounding temperature.
A continually-pulsed mode of measuring DC beta
suggests itself for conditions that might otherwise
limit the accuracy of the results due to a change
in temperature. For determining DC beta under a
wide variety of operating conditions few methods
can do better than plotting one or more curves
to show the entire forward transfer characteristics
for the particular transistor being used in the
measurement. Transistor curve tracers do that
rapidly.
Fig. 1-1 shows the collector current which flows as
the collector voltage of a transistor is swept between
zero volts and ten volts by a fullwave rectified
sinewave after a specific base current of 50 ~A has
been applied. The DC beta can be determined for any
point on the curve by reading the collector current
at that point from the calibrated vertical scale,
then dividing that current by the base current
selected. An alternate way is to first determine what
the beta per division is for the vertical scale,
and read DC beta directly from the scale. For
example, the beta per division in Fig. 1-1 is 20,
the quotient of 1 rnA (collector current per division)
and 50 ~A (the base current per step).
If the purpose in measuring the DC beta of the
transistor shown in Fig. 1-1 was to see whether it
exceeded 180 when the collector voltage was
5 volts and the base current was 50 ~A, the
measurement would consist simply of observing whether
the curve was above or below Point A, the ninth
division at the center vertical graticule line,

4

POINT A

10

8

I

Ie

(mA)

6
4
2
0

0

2

V

c

4

.. +rvvY\

6

8

(VOLTS)

10

0

+
JL.JL
0
CURRENT
STEPS

B

VOLTAGE
SWEEPS
E

Pig. 1-2.

go, no-go
testing

hpE , 2N3904 53-~A base-current step
(50 ~A plus 3 ~A of offset) .

because the ninth division corresponds to a beta of
180, and that line corresponds to 5 volts.
Such a
measurement may also be considered a test; a
quantitative test. Rapid go, no-go testing may be
performed without ever making a reading from the
scale or recording a number.
Fig. 1-2 shows the same transistor passing a
collector current of precisely 9 rnA at 5 volts,
slightly more than in Fig. 1-1. This collector
current was achieved by increasing the base current
slightly. To determine the DC beta under this set
of conditions the collector current should be
divided by the base current as before. The only
difference is that DC beta would now be determined
at a specific collector current rather than at a
specific base current.

5

avoid
heat
influence;
shorten
duty
factor

Measuring DC beta at high currents or high collector
voltages in the foregoing way may increase the
temperature enough to influence the validity of the
measurement. The temperature may be considerably
reduced by reducing the percentage of time the
transistor is turned on. This may be achieved in a
couple of ways. One way is to plot a single-shot
curve (single family). A push button or lever
switch may be provided for this purpose, and applies
base current for only one half of one complete
alternation of the power line per curve, 8.3 ms or
10 ms depending on whether the power line frequency
is 60 Hz or 50 Hz. Base current drive is removed
except momentarily when the pushbutton is depressed.
See Fig. 1-3.

1.0

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1

.6

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CA)

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0
2

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Ve

4

3

(VOLTS)

5

~

+rvvY\
0
CURRENT
STEP

B

VOLTAGE

SWEEPS
E

Fig. 1-3.

hFE, 2N3904 single-shot curve.

hFE = 5.8, when Vc = 2.5 volts.

6

very short
duty factor

Applying enough base current to induce a high
collector current to flow for 1/120th of a second
is sometimes long enough to burn out a small
transistor, particularly when collector voltage is
also high. To determine current gain for
exceptionally high collector voltages or collector
currents requires turning the transistor on for
even shorter intervals of time. Fortunately this
can usually be done repetitively at a very low duty
factor, so that the average dissipation is low.
Pulses of specific amounts of base current may be
introduced for intervals as low as 80 ~s at a
repetition rate as low as 50 or 60 Hz on the
Type 576 Tektronix Curve Tracer.
See Fig. 1-4. Peak power delivered under these
conditions is more than 200 times greater than the
average power.

1.0

.8

t
I

C
(Al

.6
.4

0

2

V

c

(VOLTS)

3

4

5

.6~

+ -.-LU...L

a

EQUAL
CURRENT
PULSES

Fig. 1-4.

B

hFE, 2N3904 repetitively pulsed while
manually scanned once.

7

pulsing
the base
current

learn
heat
effect
before
measuring

temperature
rises unti I
heat out
heat in

When this method is used the base current may be
pulsed at moments when the swept collector voltage
is near its peak value. Or a DC voltage, which may
be manually varied, may be applied to the collector.
Either way the transistor conducts only a small
percentage of the time, at moments when base current
pulses are applied. The collector voltage may be
set to plot DC beta at a particular collector
voltage, or it may be manually varied to simulate
a curve. Fig. 1-4 is a time exposure showing the
whole range of collector voltages below 5 volts as the
collector voltage supply is varied with the peakcollector-volts knob.
Sometimes the main problem with dissipating heat when
measuring the characteristics of a transistor is
knowing that you have a problem! Usually with a
transistor curve tracer you may determine when heat
dissipation becomes significant by simulating the
measurements at lower currents and voltages, and
increasing drive until the effects of heat become
apparent. This procedure may require operating the
transistor at higher collector voltages or with
greater collector current than the test or
measurement calls for before the effects are noticed.
When it does, of course, the conditions for the
desired measurement do not involve a significant
heat effect. Reasonable care should be taken to
not exceed collector breakdown voltage, or to use a
resistor in series with the collector supply that
has a high enough value to limit collector current
to a safe value if breakdown is exceeded. Should
the effects of excessive heat become apparent when
even less power is dissipated than required for the
measurement, the method of making the measurement
will usually need to be changed.
Whenever peak collector voltage is high, more heat
is produced. How rapidly heat may be dissipated from
a transistor will depend on the transistor construction
and what method, if any, is used to transfer the heat
away. The first hurdle in getting heat out of a
transistor is transferring the heat developed in the
semiconductor material to the case of the transistor.
Temperature will build up rapidly in a transistor
whenever a larger amount of heat is generated than
can escape rapidly. Temperature invariably increases
until the heat escapes at the same rate it is being
generated!

8

overheat
symptoms

Knowing how to recognize symptoms of excessive heat
is important. Probably the best procedure to follow
is to increase the collector sweep voltage slowly
while observing the resulting curves.
If at any
time while increasing the maximum collector voltage,
any curve is not simply an extension of the curve
depicted with less peak collector voltage applied,
there is probably excessive heat. Usually when an
increase in temperature becomes significant, the
curve will shift toward a different set of collectorcurrent values. This can be observed quite readily
while varying the peak collector voltage slowly.
See Fig. 1-5. This photograph is a double exposure
showing a repetitively swept peak collector voltage
of 2.5 volts for the top curve and 5 volts for the
lower curve. Notice also the prominent loop in the
longer curve. This loop indicates a significant
change in junction temperature during the time of each

1.0

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I

t-:
.

C
(A)

.2

o

o

123

V

c

4

5

~

(VOLTS)

+NVY\
o

+JLJL

o

CURRENT
STEPS

VOLTAGE
SWEEPS

B

E

Fig. 1-5.

hFE , 2N3904 effects of temperature.

9

sweep. It is apparent in Fig. 1-3 also, even though
the average temperature of the transistor is much
less in Fig. 1-3 than in Fig. 1-5.
Fig. 1-6 shows the same transistor being tested as
shown in Fig. 1-5, except less heat is being generated.
Reduced base current drive, and consequently reduced
collector current, account for reduced heat. Also
peak collector voltage was reduced from 2.5 volts to
1 volt. Notice how the longer curve is close to
being a simple extension of the shorter curve,
compared to Fig. 1-5.
When it is necessary to measure the DC beta of a
transistor under conditions where temperature is
affecting the measurement, there are only two
approaches to the problem -- either reduce the energy
input to the transistor, or get rid of the heat
faster. Both may sometimes be necessary.

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CURRENT
STEPS

B

VOLTAGE
SWEEPS
E

Fig. 1-6.

hFE' 2N3904 effects of reduced
temperature.

10

T ri se
fast with
low mass

The first thing that may normally be done to reduce
the heat generated under test conditions used for
Fig. 1-5 and Fig. 1-6 is to reduce the repetition
rate of the base current step generator from 50 or
60 Hz to a one-shot basis. This way, only once each
time a pushbutton or lever switch is activated, is
the selected base current applied. The base current
pulse would be applied for only half of the period
of one cycle of the line frequency -- usually 8.3 ms
or 10 ms. Large power transistors do not normally
change temperature appreciably in 10 ms, so one-shot
testing of them is generally a satisfactory method.
Low-power, low-mass transistors may change temperature
significantly during 10 ms. When this happens the
curve will consist of a loop instead of a single trace.
See Fig. 1-3 and 1-7 for a comparison of two
transistors rated for different power. Both are

+(ffl\
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CURRENT
STEPS

B

VOLTAGE
SWEEPS
E

Fig. 1-7.

hFE , 2N344l reduced temperature change
for power transistor at comparable
peak power.

11

temperature
hysteresis

it's hotter
than you
think

dissipating about the same peak power. Notice the
distinct loop for Fig. 1-3. The loop is caused by
junction temperature rising as collector voltage
rises towards a peak value. As the collector sweep
voltage drops back down from its peak value, the
transistor is hotter than while the collector voltage
was rising. The retrace does not coincide with the
forward trace because less collector current passes
when the transistor is hotter -- all other conditions
being equal. The case of a transistor does not have
to be warm to the touch for the internal semiconductor
material to momentarily reach a high temperature.
Poor thermal bonds may be detected this way by
comparison with a similar transistor that has a good
thermal bond.
To measure DC beta of low power transistors where
very high peak power is generated, we must reduce
the time intervals during which the transistor is
conducting to much less than 10 ms. Fig. 1-4 shows
a plot of the DC beta of the same transistor as used
in Fig. 1-3. The photograph is a time exposure
produced by slowly reducing the collector voltage
to zero while equal value base current pulses 300 ~s
wide are applied.
Some curve tracers will not display as few as two
curves at a time for a transistor, the way the curves
have been illustrated. These illustrations show a
principal curve depicting a range of collector currents
at a selected base current and an incidental curve
showing the collector current resulting from zero base
current. The Tektronix Type 575 Curve Tracer shows a
minimum of five curves, under similar conditions, one
depicting collector current for zero base current,
plus four others depicting collector current for
discrete amounts of base current. To measure DC
beta with displays of this kind you need only to
ignore all curves but the one corresponding to the
base current of interest. The base current of interest
corresponding to anyone of the curves is determined
by multiplying the selected base current per step
(amount of current increase per step) times the
number of steps required to produce that curve.
For example, if we were interested in the fifth
curve (fourth above the zero base current curve),
and the base current increase per step was 20 rnA,
we would mentally multiply 4 x 20 to determine that
80 rnA of base current was applied when that curve

12

1.0

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CVOLTSl---t~~

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fV\fV\

o

CURRENT
STEPS

B

VOLTAGE
SWEEPS
E

Fig. 1-8.

hFE, MPS9l8 DC beta from a family of
curves. Four steps at 20mA per step.
High temperature may reduce collector
current.

was produced.
See Fig. 1-8. The curve corresponding
to zero base current is usually a straight line and
sometimes not considered a curve. The number of steps
from zero is the correct number to multiply by the
current per step. The reduction in beta due to
increased temperature is apparent because of the
negative slope of the top curve.
When more than one curve is displayed other than the
zero-current curve, we say a family of curves is
displayed.
If a set of curves is displayed only
once, we say it is a single family display.
Sometimes a single family must be displayed to look
at a particular curve.

13

singlefami Iy
procedure

static may
not mean
static

know
conduction
time and
duty
factor

trans istors
not static
components

To limit temperature rise as much as possible with
a single family display, the curves in the family
should be as few as possible, and the curve of
interest should be the one depicting the highest
current.
If the top curve cannot be selected to
represent the desired base current, then a curve
which can be made to represent the desired base
current should be selected, and it should be as
close to the top as possible.
Some people will sense a sort of dilemma when they
consider the need to limit the temperature rise of
a transistor while measuring its static forward
current transfer ratio.
If the measurement is
conducted to predict how a transistor will operate
in a circuit under static conditions which are such
that transistor temperature is bound to rise
considerably, we should see that the term "static
forward current transfer ratio" is sometimes a
misnomer. Measurements of static characteristics
on a repetitive transient basis may fail to predict
that the transistor could behave differently or even
burn out if operated at a higher duty factor or for
longer conduction intervals than used in the
measurement technique.
For this reason it is
sometimes important to know the conduction time and
duty factor used in the measurement.
The duty
factor is determined by dividing the conduction
time in each cycle by the time interval of each
cycle. That decimal fraction is then multiplied
by 100 to express the answer as a percentage.
The measurement of the static forward-current transfer
ratio, or the DC beta, of a transistor may be thought
of in slightly different terms for greater clarity.
Transistors are not used as static components; they
are generally used for their ability to change
current flow.
What we really want to know when we
measure the "static" forward current transfer ratio
of a transistor is either 1) how much current the
collector can deliver at any given collector voltage
with a particular amount of base current, or 2) how
much base current drive it takes for the collector
to deliver a particular amount of current at a given
collector voltage. Naturally the more peak power
you want out of a transistor, the more limited its
conduction duty factor has to be. The smaller the
transistor is the more we have to tolerate shorter
conduction intervals as well as limited duty factor.

14

hFE(INV) -- Static Forward Current Transfer Ratio
(Collector And Emitter Leads Reversed)
reverse
terminals

Some transistors may be operated with the collector
and emitter leads interchanged. When this is done
the base-collector junction is forward biased, and
the base-emitter junction is reverse biased. Most
circuit designs do not deliberately use this mode
of operating a transistor. However, a difference
in characteristics in the saturation region is
sometimes favorable for circuit design considerations.
Typically DC beta is not as high in the reverse
direction.

POINT A

t
2

0

6

4

VeE (VOLTS)

10

8
~

~NVVI
+ .JLIl..

a

CURRENT
STEPS

B

VOLTAGE
SWEEPS
E

-::

Fig. 1-9.

hFE(INV) , 2N3904.

15

hFE>h FE ( INV)

Transistors made to have very similar characteristics
when the collector and emitter terminals are reversed
are sometimes called bi-directional transistors, or
symmetrical transistors. Fig. 1-9 shows a plot of
hFE(INV) for the same transistor as used in Fig. 1-1.
A comparison of the two figures will show that for
all collector voltages, hFE(INV) is much less than
the value of hFE . At point A the beta is 2. All of
the measurement techniques and considerations that
apply when measuring hFE may be used for measuring

hFE(INV)'

Small-Signal Short-Circuit Forward Current
Transfer Ratio (Common Emitter)
most
common
parameter
h fe

measure
AC beta
output AC
short;
output Z
low

h

fe

:

The small-signal short-circuit forward current transfer
ratio, AC beta, or current gain of a transistor for
small input signals of low frequency, is probably
the most common transistor characteristic for which
there is use and concern. It is the characteristic
that lets us predict voltage gain or power gain in
some circuits. As with DC beta, AC beta depends
on where within the normal operating range the
measurement is made. Therefore, measurements of
small signal current gain should be made under
specified conditions. Collector voltage should
be known and either average base current or average
collector current also known.
Measurements of AC beta should always be made at the
specified collector voltage, even though small
percentage deviations in collector voltage typically
produce extremely small errors. An expression of the
need to measure output signal current at only the
specified collector voltage is made when we say that
the output must be AC short-circuited. That is
another way of saying the output impedance must be
very low as far as the output signal is concerned.
Otherwise, the collector voltage will be altered
by the changes in collector current, and thereby
reduce the changes in current.
Implicit in the term "small signal forward current
transfer ratio" is the idea of signal amplification.

signal
ampl ification And most small test signals are sinusoidal, so we

are often lead to conclude that a measured amount
of sinusoidal signal current must be applied, and
the resulting sinusoidal output signal current must
be extracted and measured to determine the current

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IB

Fig. 1-10.

Transistor curve tracer block diagram.

VERTICAL
AMPLIFIER

17

transfer ratio, or current gain. Although there is
nothing wrong with such a technique, there are
other ways to make the measurement that are
sometimes more practical.

ratio of

changes

When we apply an alternating input signal current
we simply add to, then subtract from, the base bias
current that is already applied; there can be only
one amount of base current at any instant. So it
is a change or difference in base current that we
are inducing when we apply a signal current and it
is the resulting change or difference in collector
current that we need to measure. Knowing the change
in base current and the resulting change in collector
current we can determine the transfer ratio, whether
the changes are sinusoidal or some other shape as
long as the collector voltage is known, and the rate
of change slow enough so the high frequency
limitations don't start to take effect.
Transistor curve tracers introduce changes in base
current in the form of equal-value steps; steps of
selectable known amounts. These steps occur at the
same rate as the collector supply voltage is swept
between zero volts and some peak value and back to
zero, producing a separate curve corresponding to
each different value of base current. See Fig. 1-10
for a functional block diagram of a transistor curve
tracer. When the curves which are plotted depict
collector current vs collector voltage for different
values of base current, the change in collector
current induced by one step of base current will be
proportional to the vertical distance between
adjacent curves, and can be read directly from the
scale. Which vertical line is chosen for the scale
will depend on what collector voltage was specified,
because each vertical line corresponds to a
particular collector voltage.
(However, the whole
display can be positioned a particular amount when
desired to make a particular collector voltage
appear on a line having small graduations.)
Measurement of the small-signal short-circuit forward
current transfer ratio of a transistor using a
transistor curve tracer consists of the following
procedure:
1.

Choose the vertical line corresponding to the
specified collector voltage;

18

reading
the
curves

2.

Note on that line the distance between the
two curves which appear above and below the
specified base current (or specified
collector current) and lie adjacent to the
specified current;

3.

Translate that distance to the difference in
collector current according to the current
per division of the scale;

4.

Divide that collector current difference by
the base current difference that caused it,
depending on the current per step.

An alternate way is to first divide the collector
current per division by the base current per step to
determine the beta per division. For example, base
current steps of 1 rnA per step, that produced curves
1 division apart when the collector current per
division was 100 rnA, would indicate a small-signal
current gain of 100. Under similar conditions, if
the distance between curves was 1.4 divisions, the
current gain would be 140. The Tektronix Type 576
Curve Tracer will indicate the beta per division of
the vertical scale so that it doesn't have to be
computed.

"sma II
signal"

constant
current
gain

When measuring small-signal short-circuit current
transfer ratio in the way just described, attention
should be given to the size of the small signal. A
reason for distinguishing between small-signal AC
beta and large-signal AC beta is that current gain
is sometimes different for small signals than it is
for large signals. How small is a small signal?
When we carefully define a small signal using numbers,
the definition is somewhat arbitrary. In general,
however, a small signal is one which is associated
with a current gain that is essentially constant for
all smaller signals. That also tells us current gain
for large-signals depends on the size of the signals.
The same thing which causes a difference between
current gain for large signals and current gain for
small signals causes a change in gain for small
signals if we change the base bias current. In other
words, a given difference in base current, starting
with high base current, may not cause the same
change in collector current as if that change in
base current were made starting with low base current.

19

When there is a considerable difference in current
gain, the effect is readily apparent on a transistor
curve tracer by the difference in vertical distance
between the curves. Regions where the curves are
closer together are regions of lower current gain.
See Figs. 1-11 and 1-12.
Typically, as shown in Figs. 1-11 and 1-12,
transistors have lower current gain at high values
of collector current (and very low values of
collector current) than for medium values.
Fortunately transistors don't usually have to be
operated at high values of average collector current
when they are only called upon to handle small
signals.
100

80

r

I

C

40

(rnA)

20

o
2

3

VCE (VOLTS)

+/

4
~

~NVV\

0

CURRENT
STEPS

B

VOLTAGE
SWEEPS
E

Fig. 1-11.

Beta nonlinearity MPS918,
0.1 rnA per step.

5

20

1.0mA
100

80

t
I

C

60
40

(rnA)

20

I i near

versus
non I i near

Another, but similar, reason for distinguishing
between large-signal current gain and small-signal
current gain is to distinguish between a linear and a
nonlinear range of operation. A nonlinear range can
cause signal distortion. AC methods of measuring AC
beta may obscure distortion-causing nonlinearities
that can be revealed by other methods of testing. The
reason is that when sinusoidal signal currents are
applied to the base of a transistor, the change in
base current is both an increase and a decrease from
the average or quiescent base current amount. A
condition where an increase in base current produces
less of a change in collector current than an equal
decrease in base current will cause a distorted output

21

waveform. But the amplitude of the waveform may not
change appreciably. When that happens it is because
the reduced current gain for the increasing half of
the base current signal was nearly matched by the
increase in gain during the other half cycle of the
base current signal. DC methods of measuring smallsignal current transfer ratio are sometimes superior.
See Fig. 1-13. Here we can readily notice a
difference in the vertical distance between curves at
the vertical centerline signifying a change in beta
for each of the base current steps. Consider a
sinusoidal base current signal superimposed on a base
bias current of 6 rnA corresponding to curve B. If its
peak amplitude were equal to one base-current step
(2 rnA) the peak-to-peak collector-current swing at the
CURVE A

c

B

.5

i

.4

.3

Ie

(A) .2

.1

o
o

2

V

c

CURRENT
STEPS

3

(VOLTS)

4

5

..

~ rYm
B

VOLTAGE
SWEEPS
E

Fig. 1-13.

Beta, hfe.

22

centerline would be 3.0 divisions. Doubling the base
current to a peak value equal to two steps would
double the collector current swing to 6.0 divisions.
Because 6.0 is precisely equal to twice 3.0, we would
normally assume that the AC beta was constant for
input signals having a peak amplitude of 4 rnA or less.
The curve tracer reveals a measurable change in beta
for signals only half that size. For example, the
distance between curve B and curve A is 1.4 divisions,
whereas the distance between curve B and curve C is
1.6 divisions. The beta per division is 20 so the
small signal beta for the two steps is 28 and 32
respectively. The small signal beta correctly
measured by AC methods would have been half way
between the two or 30.

base
current
versus
col lector
current

Another way to measure the forward current transfer
ratio using a curve tracer is to plot base current
against collector current using base current as one
of the coordinates. There can be a problem with this
method in knowing what part of the curves correspond
to a given collector voltage. The peak collector
voltage varies from sweep to sweep, because of the
inevitable IR voltage drop caused by collector
current and the combined resistance of the
collector-sweep supply and the collector-currentsensing resistors in series with the supply.

h fb

--

Small-Signal Short-Circuit Forward Current
Transfer Ratio (Common Base)

In most cases the measurement of alpha, the forward
current transfer ratio of transistors operated in
the common base mode, can be done more accurately by
making the measurement in the common-emitter mode,
and converting the answer by formula to the commonbase mode.
h

h

fb

fe
1 + h

fe

A beta of 10

equals an alpha of 0.91;

A beta of 20

equals an alpha of 0.95;

A beta of 50

equals an alpha of 0.98;

A beta of 100

equals an alpha of 0.99.

23

.5

t

.4

I

.3

Ie
(A)

.2

.1

o
024
6
V (VOLTS)

e

o~
CURRENT
STEPS

Pig. 1-14.

ha rd to
measure
alpha
precisely

8

10

~

+

o

rvvY\

VOLTAGE
SWEEPS

Alpha, hpB'

A two-to-one change in beta from 50 to 100 corresponds
to only a one per cent change in alpha. This says we
have a very tough measurement to make with precision
if we wish to measure alpha directly. Nonetheless,
Fig. 1-14 shows a family of curves depicting
collector current versus collector voltage with the
current-step generator driving the emitter. The
display illustrates how nearly equal to emitter
current the collector current is for an average
transistor.
Each current step is equal to the current
per division of the vertical scale. The top curve
falls short of being coincident with the top of the
scale by 3%, indicating a DC alpha of 0.97 if we
assume that the instrument is perfect. A small error
in the accuracy of the instrument could account for a
gross error in measurement. Any deviation in the
small-signal alpha from large-signal alpha is nearly

24

impossible to discern. The extreme equality of
separation between the curves suggests that groundedbase operation is capable of providing very linear
output voltage swing.
h

fc

-- Small-Signal, Short-Circuit Forward Current

Transfer Ratio (Common Collector)

The measurement of this parameter is conducted by
first measuring beta under specified conditions, and
adding one (1) to the answer. The common-collector
mode is similar to the emitter-follower configuration
where the emitter is the output terminal. Since
emitter current is always the sum of the base current
and the collector current, the change in emitter
current which accompanies a change in base current is
the base current plus the collector current. Because
beta is the ratio of collector current to base
current, a unit change in base current causes beta
times that much change in collector current.

SATURATION VOLTAGE AND CURRENT
VCE(sat) -- Collector-to-Emitter Saturation Voltage, DC

saturation
region

A transistor biased normally and operating in the
common-emitter mode is said to be in saturation when
there is too little collector voltage applied (or
remaining) for an increase in base current to cause a
significant increase in collector current. On a
graph of a transistor showing collector current versus
collector voltage for a particular base current, the
saturation voltage is the collector voltage at a
point near or below the knee. On a graph showing a
family of such curves the saturation region is an area
of low current and voltage below the knee of each
curve. See Fig. 1-15. From this family of curves we
can see that the knees of the curves occur at
practically the same collector voltage for different
amounts of collector current.

25

POINT A
5

4

t

3

Ie

(rnA) 2

26

5

4

3

2

Fig. 1-16.

Saturation region.

Fig. 1-16 shows the saturation characteristics of a
different type of transistor using identical test
conditions and scale factors. Notice the lower
saturation voltages for this transistor than for the
one whose characteristics are graphed in Fig. 1-15.

V
CE (sat)
at low
power

Measurement of collector-to-emitter saturation voltage
at low power can be done quite readily using a
transistor curve tracer with the kind of display shown
in Figs. 1-15 and 1-16. It is well to remember,
however, that both the base current and collector
current should be specified to identify where the
measurement should be made, if the purpose of the
measurement is to verify a specification. If such a
measurement should happen to be at a point on a curve
above the knee, it will be of no consequence if the

27

collector voltage is not excessive because saturation
voltage is usually specified to be equal to or less
than some maximum value.
Probably the most important reason for knowing about
saturation voltage is to predict the performance of a
transistor used in DC-to-AC power inverters, chopping
circuits, and logic circuits. In these applications
it is important to know how low the collector voltage
goes because at such times as the transistor is passing
the most current for the longest periods of time, and
power dissipation at the collector can quickly become
excessive. A ten per cent reduction in saturation
voltage can reduce collector dissipation by a
comparable percentage. This could allow us to deliver
extra power to the load -- which may be many times
the power dissipated by the transistor.
rCE (sat)

Collector-To-Emitter Saturation
Resistance

Saturation resistance is an expression for the
quotient of collector voltage (VC ) divided by
collector current (I C) for any given value of base
current in the collector saturation region of a
transistor operated in the common-emitter mode.
This ratio is nearly constant for some transistors
over a large range of collector current values.
When it is fairly constant, collector saturation
voltage can be estimated quite accurately over the
same range at the given base current or higher
base currents. A constant saturation resistance
would appear as a curve with a straight slope which
intersected the zero voltage and current points on
the graph. The steepness of the slope would be a
function of the x and y coordinates of the scale
and the amount of saturation resistance. The term
saturation resistance is sometimes used to mean the
dynamic resistance, or slope, at a specified voltage
or current point.
Specifications of saturation resistance are usually
for maximum tolerable values. Most measurements
of saturation resistance are for the purpose of
determining saturation voltage. With a display of
a family of transistor curves showing collector
current versus collector voltage for various base
currents, saturation voltage can be more easily

28

measured directly for nearly any combination of
circumstances. So there is seldom need to calculate
the saturation resistance except to verify a
specification.
Fig. 1-15 shows collector voltage to be 0.3 at an
emitter current of 3 rnA and a base current of 50 ~A.
The saturation resistance at that point is VclIc =
0.3/.003 = 100~. Higher base currents would show
less collector voltage needed at the same collector
current, so the saturation resistance will be less
at higher base currents. At lower values of
collector current at the given base current, saturation
resistance will be higher even though saturation
voltage at lower collector currents is always less.
Fig. 1-16 shows a different kind of saturation region,
with values for saturation resistance that differ
more widely than in Fig. 1-15.
When testing or measuring the saturation voltage of
a transistor at very high currents, pulse testing
must be used to minimize heat dissipation. Methods
may be employed similar to those discussed for
measuring the static forward current transfer ratio.

CUTOFF CURRENT AND VOLTAGE BREAKOOWN

I CBO and V(BR)CBO -- CoZZector-To-Base Current
Leakage And Voltage Breakdown,
Emitter Open

VCBRlCBO
made at
specified
temperature
and reverse
current

The measurement of reverse bias leakage current and
breakdown voltage can logically be considered at the
same time. The current that flows through the
collector-base junction when reverse biased, and
when the emitter lead is open, is very much the same
kind of phenomenon as occurs in a simple diode.
Usually that current is relatively small, until the
voltage is increased sufficiently and breakdown starts
to occur. Although the breakdown region is relatively
abrupt for most transistor junctions, a precise
measurement of breakdown voltage can only be made
at a specific reverse current and at a specific
temperature. For the same reason reverse currents
should always be measured at specified reverse
voltages and temperatures or the measurement is of
limited use.

29

100

80

20

o

o

20

V
R

UNUSED
STEPS

Fig. 1-17.

40

60

80

100

(VOLTS)----~~~

~~
VOLTAGE
SWEEPS

ICBO and VCBR)CBO, 2N918. Breakdown
region between approximately 50 V
and 70 V.

A transistor curve tracer is a simple and accurate
instrument with which to plot and measure small reverse
currents at any voltage up to the breakdown region.
The breakdown region is identified and explored at
the same time as reverse current is monitored, when
desired. A primary concern with measuring breakdown
voltage -- or measuring leakage current near the
breakdown region -- is that of destroying the junction
in the process. Transistor curve tracers allow
insertion of resistors having high resistance values
in a series with a swept voltage supply to limit reverSf
current to a safe value. The peak amplitude of the
swept supply voltage can be controlled as needed.
Fig. 1-17 shows the collector-base leakage and
breakdown region of a typical low power silicon

30

100

80

60

I

t

40

CBO
<"A)
20

0

20

0

40

V <VOLTS)
R

UNUSED

STEPS

Fig. 1-18.

60

..

80

100

~rvm
VOLTAGE
SWEEPS

ICBO and V(BR)CBO, 2N918. Abrupt
breakdown reglon between 60 volts
and 62 volts. Peak current allowed
was 100~.

transistor.
The breakdown region does not appear
abrupt in this photograph, but the breakdown voltage
is obviously between 50 and 70 volts. Another
transistor of the same type is shown in Fig. 1-18
that has a much more abrupt breakdown region.
Fig. 1-17 and Fig. 1-18 represent measurements
conducted at room temperature with no effort to control
the temperature of the transistors.
Reverse current
was limited as much as possible to make the needed
measurements.
If we wish to see the effects of
increased temperature on the measurement, we can
generate the needed heat very conveniently by slowly

31

10

8

t
I

CBO

6

4

(rnA)

2

o
V (VOLTS)
R

UNUSED
STEPS

VOLTAGE
SWEEPS
E

Fig. 1-19.

I CBO and VCBR)CBO' 2N9l8.

Identical
transistor as used in Fig. 1-18
temperature increased by increasing
peak leakage current 100X to lOrnA.
Breakdown voltage increased from
62 volts to 70 volts due to
temperature rise.

increasing the peak reverse current with the curve
tracer.
Fig. 1-19 is the same as Fig. 1-18 but
with a peak current 10 rnA instead of 0.1 rnA. The
transistor was too hot to hold. The breakdown
voltage increased from 62 volts to 70 volts. The
case temperature could have been monitored with a
thermocouple attached if we had wished to make a
measurement of its characteristics at a specific
case temperature. The junction temperature will
always be somewhat higher than the case temperature.

32

and

V(BR)EBO -- Emitter-To-Base Reverse Current,
And Vo~tage Breakdown,
Col~ector Open

The measurement of reverse current and voltage
breakdown between the emitter and base of a transistor
when the collector terminal is left disconnected is
performed in the same way as for the measurement of
leakage and breakdown between the collector and base,
already discussed. A comparison of the reversecurrent and voltage breakdown characteristics of the
collector-base junction of a transistor with the
corresponding characteristics of the emitter-base
junction of that transistor is sometimes interesting.
The breakdown region is often a lower reverse voltage
for the emitter-base junction than for the collectorbase junction.

I CEO and V(BR)CEO

I CEO and
VCBRlCEO are
diode
measurements

forward
bias
reverse
bias

Collector Cutoff Current And
Voltage Breakdown, Base Open

The reverse-current characteristics and voltagebreakdown characteristics of either the collectorbase junction or the emitter-base junction of a
transistor with the remaining terminal disconnected
is really a measurement of a diode characteristic
rather than a measurement of the transistor
characteristic. Both of those measurements are useful
for predicting some limitations of the transistor, but
the measurement of similar characteristics involving
conduction through both the collector-base and
emitter-base junctions are probably more meaningful.
The open-base condition, while also rarely encountered
in a practical circuit, does indicate a maximum, or
limit, cutoff current.
The current which flows through a transistor when the
base terminal is disconnected, and a current or voltage
supply is connected across the emitter and collector
terminals, will be forward current for one junction
and reverse current for the other junction, depending
on the polarity of the supply. When the polarity is
such that the emitter-base junction is forward biased,
the collector-base junction will be reverse biased.
Reverse bias for the collector-base junction is the
normal mode for transistor operation, and it is the
correct condition for measuring collector cutoff
current and voltage breakdown with zero base current.
The base terminal will be "floating" under these

33

conditions, and there will be a floating voltage at
the base terminal equal to the voltage-drop across the
emitter-base junction. That voltage will increase
with an increase in emitter current.
The cutoff current which flows under these conditions
is usually much greater than the reverse current
which flows through the collector-base junction when
the emitter lead is open (ICBO )' In fact, collector
cutoff current with an open base terminal is as many
times greater than collector-base reverse current
(ICBO ) as the value of the forward current transfer
ratio (for low values of collector current). In
other words, if beta is 50, then collector cutoff
current with the base open will be 51 (50 + 1) times
greater than the simple collector-base reverse current
with emitter open. The reason for the current increase
is that the reverse current through the collectorbase junction has to be supplied from the emitter
terminal, no other is available, and the carriers
injected into the base region to supply that current
diffuse and consequently allow many times that amount
of current, to pass between emitter and collector.

CUToff
current >
reverse
current

VCBRlCEO
VCBRlCBO

>

Breakdown voltage for any given amount of cut-off
current with the base open is less than breakdown
voltage for the collector-base junction alone
(emitter open). There are several factors that
account for reverse current through a PN junction
when a given reverse voltage is applied. All of
which, except for surface leakage, are temperature
dependent. When the surface leakage factor is
negligible, reverse current will approximately
double with every 6°C increase in temperature, for
silicon transistors. For germanium transistors
leakage will double about every 10°C. For this
reason careful attention must be given to temperature
when accurately measuring reverse current (cutoff
current). In some normal cases surface leakage
current will dominate.

ICES and V(BR)CES -- Collector Cutoff Current And
Voltage Breakdown, Base Shorted
To Emitter.
The collector current, which flows when the base and
emitter terminals are shorted together and reverse
voltage applied, is a small fraction of that which
flows when the base terminal is open. Under these

34

test conditions most of the collector current passes
through the base terminal rather than the emitter
terminal because the base region in the transistor
is adjacent to the collector region, and the external
short offers less opposition to current flow than the
internal emitter region.
The collector cutoff current
which flows is usually somewhat more than when the
emitter terminal is open. The resistance between
the material comprising the base region within the
transistor and the base terminal causes a small
voltage drop within the transistor that essentially
forward biases the base-emitter junction a small
amount.
The forward bias permits the emitter to
inject additional carriers into the base region and
increase the total current. Measurement of collector
cutoff current under these conditions is like
determining what collector current will flow in a,
circuit when the transistor is driven from a very low
impedance source, and the drive voltage is very cl se
to zero.

I CER and V(BR)CER -- Collector Cutoff Current And
Voltage Breakdown~ Base Returned
To Emitter Through A Specified
Resistance.

I CER fal Is
between
I CEO and
ICES

When the base terminal is connected to the emitter
terminal through a resistor instead of remaining
open or connected directly, the collector cutoff
current will be some value between what it is when
the base is open and what it is when the base is
shorted to the emitter, at any given collector voltage.
The resistor value may be selected to simulate the
source impedance of a typical base-drive circuit to
indicate what collector current would remain when
the driving voltage went to zero. The collector
breakdown voltage, VBR(CER)' for a given cutoff
current will be a voltage in between that for open
base, VBR(CEO), and that for shorted base, VBR(CES)'

I CEV and V(BR)CEV -- Collector Cutoff Current And
Voltage Breakdown~ with
Specified Reverse Voltage
If a small reverse voltage is applied across the
base-emitter terminals, collector cutoff current can
be reduced below the value which flows with the base
terminal shorted to the emitter terminal.

35

This reverse base-emitter bias will also increase the
voltage at which breakdown occurs, assuming of course,
that breakdown voltage is measured at the same
collector current value in both cases. Because some
current may flow in the base circuit under these
conditions, the resistance of the base circuit can
cause the base terminal voltage to be less than the
base supply voltage. Therefore, the base terminal
voltage should either be measured at the base
terminal or supplied from a very low resistance
source. If the supply voltage and the resistance
of the supply are known and specified the cutoff
current could be classified as ICEX instead of ICEV.

I CEX and V(BR)CEX -- Collector Cutoff Current And
Voltage Breakdown~ With
Specified Base Drive Circuit.
As has been shown by discussions of different
conditions for the measurement of collector cutoff
current, there may be a big difference in cutoff
current depending on what, if any, external connections
there may be between the base terminal and the emitter
terminal. Predicting collector cutoff current in
practical circuits may be simplified by using
simulated circuits. Such measurements provide very
good data for very similar circuits. The terms
ICEX and VBR(CEX) can be used instead of the terms
I CEV and VBR(CEV) as long as equivalent conditions
are stated.

ICEO greatest Collector cutoff current, although normally never
with Vc high, great, may be different in a given transistor
temperature

high, and
IB zero

depending on the conditions which may be said to
constitute cutoff. The highest amount of what could be
be called cutoff current flows when a transistor
has a high collector voltage, has zero base current,
and is hot. The easiest way to assure zero base
current is to leave the base terminal disconnected
or open. Collector cutoff current for this condition
is symbolically called ICEO (0 for open base). When
the base terminal is not left open, but has a resistor
of high resistance value connected externally between
the base and emitter terminals, the base terminal is
practically open but somewhat less cutoff current
flows. As the resistance value of the resistor is
reduced, cutoff current diminishes. Cutoff current
measured under these conditions varies widely,

36

depending on the value of the resistor, but is
symbolized by the letters I CER (R for resistor in
the base lead). When the resistor value between the
base and emitter is practically zero ohms, the cutoff
current is represented by the symbol ICES (S for short
circuit between base and emitter terminals).
Collector cutoff current can be diminished further by
applying a reverse voltage between the base and
emitter. The reverse voltage does not need to be
great to do its job. One or two volts is usually
adequate, when that voltage actually appears between
the base and emitter terminals. The symbol for
collector cutoff current for a reverse-biased emitterbase junction is I CEV (V for voltage between base and
emitter). The symbol ICEX could represent the same
situation, as explained earlier.

ICEV

<

ICES

Very low cutoff current flows when a reverse voltage
is applied between the collector and base if the
emitter is open. This configuration does not resemble
any ordinary use of a transistor however, so it is
somewhat of a misnomer to call it transistor cutoff
current.
It is really a measurement of a diode
characteristic -- the collector-base junction reverse
current The symbol is ICBO (0 for open emitter).

Collector Sustaining Voltage
VCEOCSUS)
VCERCSUS)
VCEVCSUS)
VCEXCSUS)

measuring
errors
near
breakdown
region

A considerable error can be made in measuring cutoff
current near the breakdown region of some transistors,
because of a negative resistance characteristic present
in this region.
In other words, one of two disti~ct
collector currents may flow with a given collector
voltage applied, depending on how the collector
voltage was chosen and applied, and whether the cutoff
current was increased to the value selected or
decreased to the value selected. With a transistor
curve tracer both points can be shown and easily
distinguished.
See Fig. 1-20 and Fig. 1-21. The
curves in Fig. 1-21 changed from those shown in
Fig. 1-20 when the peak collector supply voltage was
increased from 210 volts to 220 volts. With a
220-volt supply, avalanche breakdown occurs with
zero base current, and the collector voltage drops
to 100 volts, but sustains about 180 rnA with the
particular load used.
These curves show that when
base current is switched between zero and 3.5 rnA,
collector current will switch between about 180 rnA

37

.5

v

,,
, --

E

,

- - <

,

.4

:
,

- - <

.3

., --

R

T

0"

50

TrIA

H

0
R

I

z

20

V

OOY

~

!!!l!:l !!!!::

.2
, --

.1

!:ii !!!!! !!Ziii ,,;
!!!!!!

, --

..II

- -,

•

,

.

T

E
p

- - <

I

o

s

•

a

•

'

- - <

13

--<

9m

. ..

+

rvYV'I

~:OO

.u .Po..

s

""

100

rl!ll

COLLECTOR
SUPPLY
VOLTAGE. NO
AVALANCHE
BREAKDOWN

o

CURRENT
STEPS

B

VOLTAGE
SWEEPS
E

Fig. 1-20.

Collector breakdown, 2N4lll.

at 100 volts, and 320 rnA at close to zero volts,
if the supply voltage is 220 volts. The average
power dissipation of the transistor would be high.
With a collector supply of 210 volts or less, the
sustaining voltage would not be significant because
the avalanche breakdown would not occur.
In that
case, the transistor would dissipate very little
power because practically zero collector current
will flow, even at 210 volts, when base current is
zero.

38

COLLECTOR BREAKDOWN
SUSTAINING VOLTAGE.
ZERO BASE CURRENT

I

,
,

·-·- ·, -·, - - .'!:iii
·-.JJi 'j
.:iii

I~

v

irlj

E

,

.
.
- -.,
- -.
-- ,
--,

I
rtJ

rJ~·
m

::iiiiii

,'.

.~

•

r..

--

,

•

.
V
CE

.

~

,.

·- -

-.

- ,
,
--

.,

--,

l1

• ••

a
(VOLTS)

B

50

rnA

H

0
R
I

z
OIV

s

T

E
P

s

-t·~:

,.1..1

V

son
/.:
.u ."'\

~

o.
gm
PtR

-tOO

DIV

I
II

----J.~

+Nm
o
CURRENT
STEPS

R
T
OIV

VALANCHE
BREAKDOWN
VOLTAGE

VOLTAGE
SWEEPS
E

Fig. 1-21.

Collector avalanche breakdown and
sustaining voltage, 2N4lll.

From the shape of the zero base-current curve in
Fig. 1-21, different collector sustaining voltages
and currents can be predicted for higher values of
load resistance by using a corresponding load line.

negative R
characteristic

When there is a negative resistance characteristic in
the breakdown region, it can be detected by slowly
increasing collector voltage until the curve becomes
vertical, then turns around and starts back. Peak

39

current must be carefully limited with a high value
series resistor to avoid the possibility of
overheating the transistor. Under these conditions
increasing the peak collector-supply voltage
increases the peak collector current, which reduces
the peak collector voltage. Any collector voltage
in a (stable) negative resistance region sustains
more collector current than when the peak collector
voltage is first increased to that voltage under
otherwise identical conditions. Similarly, when a
transistor is switched from hard-on to hard-off,
that is, operated with a high collector-supply voltage
and high value series collector load resistor, the
cutoff current will be relatively high, and the
collector (sustaining) voltage relatively low.

Sustaining voltage is the collector voltage required
to sustain a given collector current where that
current is the larger of two possible values at that
collector voltage under a given set of collector-cutoff
conditions. The principal purpose for identifying and
measuring collector sustaining voltage is to indicate
how the transistor may be operated without excess
dissipation. Unless there is a negative resistance
characteristic in the cutoff region there is no object
in distinguishing between collector breakdown voltage
and collector sustaining voltage. Most transistors
exhibit no negative resistance characteristic for a
cutoff condition where the base is open. But most
do exhibit the characteristic when the base is
reverse biased, shorted to the emitter, or connected
to the emitter through any small value of resistance.

Avalanche Breakdown
avalanche:
dynamic R
drops

The term avalanche or avalanche breakdown is often used
synonomously with the term zener breakdown. Although
both terms are carefully defined in the section of this
book dealing with the definition of terms, the
distinction needed for this discussion is between
that breakdown where there is simply an abrupt
reduction in the dynamic resistance of a device or
junction, and that breakdown which is characterized
by not only an abrupt reduction in dynamic resistance,
but by a negative resistance characteristic. The
measurement of the electrical characteristics of
devices which have a negative resistance characteristic
can sometimes be plagued with errors if the negative
resistance characteristic is not known, or its

40

negative R
is evident
on curvetracer

existence not suspected. Even then control of the
measurement may be difficult and uncertain.
It is
sometimes possible to plot graphically the complete
resistance characteristics associated with collectorvoltage breakdown using a transistor curve tracer.
In cases where the negative resistance would be
represented by a very radical change in slope, it
may not be practical to swamp the negative resistance
by a comparable real resistance to plot a whole curve.
Nonetheless, avalanche breakdown does not go
undetected on a curve tracer, and even when the
precise slope of the negative resistance region is
not shown, the places where it begins and ends
will be apparent.
Whenever a negative resistance characteristic is
plotted on a curve tracer for a collector family,
as when measuring collector sustaining voltage,
for example, the negative resistance region will
be unstable if the slope of the load line
(established by the resistance in series with the
supply) is too steep. As collector current is
changed the load line should not intersect more
than one point at a time on the curve in the
negative resistance region.
When not enough series resistance is used as collector
current is increased into a negative resistance region,
the current may suddenly step to a higher value,
corresponding to lower collector voltage, at a point
where the load line does intercept the negative
resistance curve -- after that curve has bent and
become more steep. When such a step occurs, the
transition is usually rapid enough to shock exite
connecting leads into damped oscillations due to
lead inductance and stray capacitance. Even if no
oscillations occur there will be a section of the
curve that has to be considered absent. That section
will usually be easy to identify because it will be
very dim -- indicating the CRT beam was deflected
with exceptional velocity during the change from one
current value to the next.
Avalanche breakdown in some transistors can occur
in extremely short intervals of time. When it can,
then even small amounts of stray capacitance in
the leads connecting the transistor will momentarily
appear as a low impedance load to the transistor
collector.
In that case even though the current-

41

limiting resistors in series with the collector supply
may have a high enough value (to DC) to constitute a
load line that would intercept the negative resistance
curve at all points, high frequency parasitic
oscillations may prevent plotting the whole negative
resistance region.
Some transistors are used for their very fast
avalanche characteristics. See Fig. 1-22.

POSITIVE: NEGATIVE
RES ISTANCEI RES ISTANCE
I

I
I

20

t
I

16

12

4

o

VCE (VOLTS)

------J.~

+NVY\
o
CURRENT
STEPS

ZERO BIAS
AVALANCHE
VOLTAGE

B

E

Fig. 1-22.

High-speed avalanche transistor.

Selected 2N2S0l.

42

120

160

200

+(ffl\
o

VOLTAGE

SWEEPS

Fig. 1-23.

Breakdown due to reach-through,
base current steps, 2N3877A.

20~A

Punch-Through Or Reach-Through
The terms punch-through or reach-through apply to a
collector-breakdown condition where base current has
little or no influence on the collector-breakdown
voltage. The condition only applies to some
transistors, usually ones with a very thin base
region. With transistors of this type the collectorbase junction depletion region may extend all the
way through the base material into the emitter
material, when enough collector-to-emitter voltage
is applied; before some other form of breakdown
occurs. When this happens a good conduction path

43

between collector and emitter is created at a
particular collector voltage, directly through the
base material. Increasing collector voltage beyond
that value causes a radical increase in collector
current.

punchthrough
diagnosis

Breakdown due to the collector-voltage field
extending through the base material is easily
recognized on a transistor curve tracer. Whenever
the breakdown current is the same value regardless
of the base current, a transistor curve tracer will
show different curves in a collector family joining
at the breakdown region. Fig. 1-23 displays peak
collector sweep voltage limited enough to show only
the bottom two curves joining. However, all five
curves merge when collector breakdown current was
allowed to increase enough.
Reach-through is a non-destructive form of breakdown
as long as collector current is limited.

SWITCHING TIME
The speed and fidelity with which a transistor may
fully respond to a sudden discrete change in input
current has a relationship to its gain characteristics
at high frequencies -- but not a simple relationship.
While it is generally true that the transistors which
have the better high frequency characteristics are
also the ones which are faster in their response to
step signals, the best transistors for high frequency
sinewave amplifiers don't always make the best
switching circuits. This is particularly true
when the kind of switching to be done involves
driving the transistor into saturation or into cutoff.
When the drive is alternately between saturation
and cutoff, the correlation is at its worst.

switchingtransistors:
measure
vs

calculate

Even if and when all of the several individual
characteristics about a transistor that determine
its step response are quantitatively known,
predicting the performance of the transistor by
use of mathematical equations is laborious and
approximate. Testing and measuring step response
or switching time of transistors is therefore very
common.

44

Turn-On Time And Turn-Off Time
The semiconductor industry has adopted several terms
related to the switching time of transistors. First
of all, a distinction is made between the time it
takes a transistor to turn on and the time it takes a
transistor to turn off. One is called turn-on time
turn-on
= delay plus and the other called turn-off time. Both the turn-on
time and the turn-off time are divided into two
risetime
intervals, each described by a separate term. Turn-on
time is divided into delay time and risetime.
tu rn-off
Turn-off time is divided into (carrier) storage time
'" storage
and falltime. One should remember from the outset
plus
that here risetime and fa11time have nothing to do
fa I It i me
with whether the waveform being measured is positivegoing or negative-going. Risetime applies to an
risetime
- Ie increase increasing collector current. This time will be
coincident with a negative-going collector voltage
fa I It i me
waveform for an NPN transistor, or a positive-going
- Ie decrease collector voltage waveform for a PNP transistor.
Fa11time applies to decreasing collector current.

td

define delay
time and
carrier
storage time

--

De lay Time

Delay time is the time between the instant when a
current step is applied to turn the transistor on,
and the instant when collector current has increased
to 10% of its final value. To avoid any ambiguity
about the instant when a current step is applied,
measurement of delay time should be made starting at
a point on the applied step 10% of the way to its
final level.
Carrier storage time is the time between the instant
when base current is cut off, and the instant when
collector current diminishes to 90% of its full value.
Again, to make the definition and measurement of
carrier storage time more precise, the instant when
base current is cut off is said to be when it has been
reduced to 90% of its full value. See Fig. 1-24.
From this figure showing idealized wave shapes one may
erroneously infer that the fa11time of the output
pulse is about the same as the 90% to 10% fa11time
of the applied pulse. One may even infer that
risetime and fall time are usually about the same.
No implications of this kind were intended. It is
typical, however, for the risetime and fa11time of

45

I

I

APPLIED PULSE
(IOEALIZED WAVE SHAPE)

,I
I
-----------7,

10% --

I
I
I

I

:

1

I

I

:

90% - - - , - - - - - - - - - - - -1- - - - - :

:

I

I

I

I

r

I

1:

:

:

10%- __L--

___-'L.-----l:

-.1--------,-----,.-

' 11
,

1

t d :t
t
t

r:

" DELAY TIME
"RISE TIME

d

r

OUTPUT PULSE
(IDEALIZED WAVE SHAPE)

t

s
f

I

,

1

r

,r

:
t

I

t5

:

tf:

" CARRIER STORAGE TIME
~

FALL TIME

--r------PULSE
AMPLITUDE

_J_

SPIKE CAUSED BY A
CURRENT \;H ICH IS NOT
CHARGE CARRIER INDUCED

Fig. 1-24.

OUTPUT PULSE
(PRACTICAL WAVE SHAPE)

Switching transistor pulse
characteristic.

the applied pulse to be close to the same.
It is also
appropriate that the risetime and fall time of the
applied pulse be much shorter than the response
stimulated. Otherwise it would not be possible to
discern the true response limitations.
Whenever delay time is a significant portion of
turn-on time it is principally due to one or a
combination of two factors, both associated with the
quiescent cutoff condition.
Whenever the emitter-base junction is reverse biased
to create the cutoff condition, the emitter-base
junction capacitance will be charged to the
reverse bias voltage, and constitute a charge that
will have to be removed before conduction can start.
Of course, the same is true for the stray capacitance
of the emitter and base leads, both inside and outside

46

o

40

80
120
TIME (NANOSECONDS)

Fig. 1-25.

160

200

-----4~~

Turn-on characteristics of small
high-speed transistor. Six
collector voltage curves that
correspond to six base bias levels
between cutoff and saturation show
various rise rates. Turn-on delay
(td) apparent for only top curve;
collector load resistance 250~ as
in Fig. 1-28. Risetirne corresponds
to falling portions of curves.

47

of the transistor package. But this capacitance is
only of significance when the transistor is backbiased into cutoff. If cutoff is not so hard -- as
when the base current or base voltage is only reduced
near zero, there is only one principal factor. That
is diffusion time -- the time it takes carriers
injected into the base region to diffuse and let the
base region become a good conduction medium for
collector current. A transistor which is switched
out of cutoff, but not into saturation, will exhibit
as much delay time as if it were switched into
saturation. Delay time is usually minimal when the
transistor is barely cutoff, and then is turned on
hard. In Fig. 1-25 we have shown the collector
waveforms that result when a fast-rise turn-on pulse
approximately 12 ns wide and 2 volts tall is applied
to the base of an NPN transistor through a
non-inductive lOOO-ohm resistor. An oscilloscope
rather than a curve tracer was used. The transistor
was biased at six different levels including
saturation and cutoff. Only the top curve represents
a quiescent cutoff condition. The bottom curVe shows
the applied pulse and the curve next to the bottom
represents the transistor biased into saturation
before the turn-on pulse was applied. Notice that
none of the curves show any turn-on delay except the
top curve, where about 1 minor division (or 4
nanoseconds) of delay is apparent.

t r -- Risetime
Risetime (the negative slope on the collector
waveforms in Fig. 1-25), cannot be measured from
these curves because the turn-on pulse did not last
long enough. But the curves illustrate other things.
Even though each curve represents the same increase
in base current (2 rnA) a considerable difference in
slope and amplitude can be seen for the different
curves, particularly as collector voltage approaches
saturation. This should show us that the change in
slope is due to a change in collector voltage. The
top curves show a relatively linear rise rate
because collector voltage saturation has not been
reached. When these curves are allowed to continue
toward saturation by making the turn-off pulse last
longer they also become rounded, but it is difficult
to tell from those curves alone whether the rounding
reveals a basic RC type of characteristic or not.
Risetime is primarily limited by the collector-base
junction capacitance, ana all stray capacitance
between the collector and base leads, plus the

48

input
capacitance
change
z

l1VC
l1VB

virtual
input
C »
actual C

illL
dt

amount of base current available to discharge that
capacitance. When the collector voltage changes as
a result of changing the collector current -- as it
will unless the load impedance is zero -- the
collector-base capacitance is, in effect, increased
in proportion to the change in collector voltage.
The magnitude of the increase is limited by the
reverse voltage transfer characteristics of the
transistor, and is approximately equal to the ratio
of the change in collector voltage to the change in
base voltage.
This figure can be very large.
In
essence, current in the base lead must discharge the
collector-base capacitance as the collector voltage
decreases.
So, when current in the base lead is
suddenly increased to a new level, most of the
increase is at first diverted to discharge the
collector-base capacitance. This delays the
increase of carriers in the base region, which
accounts for most of the risetime.
The rise rate
is linear except in the region near saturation,
because a practically constant current discharges a
practically constant capacitance.
Collector-base
junction capacitance will typically increase as the
collector voltage reduces, however, and this also
accounts for a slope that is less steep for lower
values of collector voltage.
The importance of collector-base junction capacitance
as a limiting factor on transistor risetime was
discussed. The fact is emphasized that the actual
capacitance values may be only a small fraction of
the virtual capacitance which must be discharged by
base current.
Stray capacitance, due to circuit or
socket capacitance, between collector leads and base
leads can account for a poor correlation of
measurements between otherwise identical test
fixtures when measuring risetime or rise rate.
Some people will prefer measuring rise rate to
measuring risetime when evaluating the turn-on time
of a transistor. Rise rate would be expressed in
terms of volts per unit time, but might be measured
by determining the time it takes for the slope to
cross two discrete voltage levels.
t

s

Carrier Storage Time

Fig. 1-26 is similar to Fig. 1-25 except that a
turn-off pulse was applied instead of a turn-on
pulse.
The applied turn-off pulse is shown on the
bottom curve to establish when turn-off commences.

49

UTOFF LEVEL
COLLECTOR

CURVE 5
TURN-OFF PULSE
12ns WIDE,
2V TALL

o

40

80

120

TIME (NANOSECONDS)

Fig. 1-26.

160

200
~

Turn-off characteristics of small
high-speed transistor. Five
collector-voltage curves that
correspond to five base bias levels
between saturation and cutoff.
Carrier storage time (t s ) apparent
in curve 5 is partly due to
quiescent saturated condition.
Conditions similar to Fig. 1-25 and
Fig. 1-28. Turn-off pulse is 2mA
(Two volts across 1 kn).

50

The collector curves are of the same NPN transistor
as used for Fig. 1-25 and the beginning of turn-off
is represented by the up-going portions of those
curves. The curve adjacent to the bottom curve is
the only curve representing a quiescent saturated
condition. Notice that this curve is the only one
which does not appear to start to respond the
instant the turn-off pulse is applied. Because the
turn-off pulse is only about 1.2 volts in amplitude,
and it can reduce base current by only about 1.2 rnA
(through a 1 kQ series resistance), the collector
could not be saturated very much and still show the
influence of only a 1.2 rnA reduction in base current.

t s - storage

time

See Fig. 1-27. To show a delay in response to a
turn-off pulse, the drive pulse amplitude was
increased so that the transistor could be saturated
harder and the turn-off pulse still be able to reduce
base current enough to let the transistor come well
out of saturation. The time scale was reduced from
20 nanoseconds per division to 5 nanoseconds per
division, to avoid crowding the curves. The four
top curves are produced under identical conditions
except that the quiescent bias current was changed.
The top two curves represent bias levels that allowed
the transistor to remain out of saturation. These
two curves show essentially no delay in response to
the turn-off pulse. However, the bottom two collector
curves represent a saturation condition, and show a
delay in response to the turn-off pulse. The curve
which shows the greater delay represents the more
saturated condition. This delay in response to
turn-off is called carrier storage time, or simply
storage time (t). As the term implies, the delay
is attributableSto an excess of carriers someplace.
The excess carriers are primarily in the base
material unless the collector-base junction becomes
forward-biased in saturation. The primary reason for
the excess is that collector voltage has been reduced
so greatly by the voltage drop across the collector
load resistor, that an insufficient voltage remains
to collect all of the carriers that have become
mobilized. These excess carriers will eventually
disappear due to collector current, and by
recombination with others of opposite polarity within
the semiconductor material. Storage time will be
less if new carriers are not created by allowing some

51

CUTOFF LEVEL
A

B
C
D

TURN-OFF PULSE

o

20

10

30

TIME (NANOSECONDS)

Fig. 1-27.

50

40
~

Turn-off characteristics of small
high-speed transistor using 6mA
turn-off pulse. Four collector-voltage
curves corresponding to four bias
levels. Turn-off corresponds to
rising portions of curves. Curves
C and D show storage time (ts), a
delay in response to turn-off pulse,
due to beginning in saturated
condition. See Fig. 1-28 for circuit.

52

cutoff pulse
high and
fast reduces
t

s

residual base current to continue to flow.
In other
words, the applied cutoff pulse will reduce carrier
storage time if it is high in amplitude as well as
fast in transition time. When the turn-off pulse is
more than tall enough to reduce base current to zero,
the direction of current flow in the base lead will
reverse and tend to back-bias the emitter-base
junction. This momentary reverse current ~ill speed
up removal of excess carriers, too.
It is worthwhile noting that the carrier storage time
represented by the middle two curves in Fig. 1-27
far exceeds the risetime of the leading edge of the
turn-off pulse.
If the risetime of the turn-off
pulse had not been much shorter than the storage
time, there could be a considerable difference in
the display and the measurement of storage time.
t

fa I I time:
same factors
as risetime

f

--

Fall Time

Fall time is determined by essentially the same
factors that determine risetime.
Refer to the
paragraphs on risetime for that discussion.
Figs.
1-25 and 1-26 show the same transistor under nearly
identical test conditions, except Fig. 1-25 shows
response to a turn-on pulse whereas Fig. 1-26 shows
response to a turn-off pulse. Compare the falling
slopes (risetime) of Fig. 1-25 with rising slopes
(fall time) of Fig. 1-26.
Fig. 1-28 shows a simplified diagram of the test
circuit used to produce the curves photographed and
shown in Figs. 1-25, 1-26 and 1-27.
COLLECTOR
SUPPLY
PULSE MON I TOR
(TERMINATE
\~ITH 500)

INPUT
PULSE

950

JL

~~

T

950

@
~

lk

50

250
OUTPUT
(TERMINATE
WITH 500)

5k

BASE BIAS
SUPPL Y

Fig. 1-28.

Simplified switching-time test
circuit.

53

INPUT CAPACITANCE
C.les ,C l'b s ' C.leo ,C l'b 0

ies - input,
commonemitter, zero
fJ output
ibs - input,
common-base
zero fJ output

The input capacitance of a transistor will depend on
whether the transistor is operated in the commonemitter mode or the common-base mode, and it will
depend on the value of the load impedance. The
symbols Cies and Cibs are used when the output load
is zero ohms (output short circuited). To symbolize
input capacitance under the opposite extreme of
output load resistance (output open circuited), C ieo
and Cibo are used. The symbols, therefore, stand
for boundary conditions that cannot quite be
realized in practice in any case.
The input capacitance of amplifying devices like
vacuum tubes and transistors is of interest to a
circuit man because that capacitance has a bearing
on the high frequency response or switching time of
his circuit.
In particular it will give a clue to
the loading effects on whatever is used to drive the
input of the amplifying device. With vacuum tubes,
which are voltage-controlled devices ideally having
a high input impedance under all conditions, input
capacitance will predominate at even audio
frequencies when the driving impedance is high.
With transistors, that are current-controlled and
have an input impedance that is low compared to
vacuum tubes, input capacitance has a somewhat
different significance.

trans i stor
vs triode

To a very limited extent the plate-grid capacitance
of a triode is comparable to the collector-base
junction capacitance of a transistor. And to the
same limited extent the grid-cathode capacitance is
comparable to the emitter-base junction capacitance
of a transistor. These two capacitances plus
voltage gain are practically all that need be known
about a vacuum tube to predict its input capacitance.
With transistors, however, several things are
radically different:

1.

real C and
virtual C

2.

Collector-base junction capacitance changes with
collector-base voltage.
Emitter-base junction capacitance may have very
little change in charge because base-emitter
voltage typically changes slightly when the
transistor is turned on.

54

3.
4.
5.

Carrier diffusion time acts like capacitance.
Carrier recombination time acts like capacitance.
Some of the real and the virtual capacitances
have considerable resistance to charge and
discharge through.

Because of the equal importance of these other various
characteristics, input capacitance is usually
estimated by measuring the two junction capacitances
using a capacitance bridge. Input impedance or
admittance measurements at various frequencies under
various operating conditions using RF bridges are
used fer a more complete picture. Bridges are
offered commercially that permit high frequency
measurements to be made beyond 1 GHz.

OlITPlIT CAPACITANCE

output C vs

HF
performance

The output capacitance of transistors, similar to
input capacitance, depends on a complex variety of
things. Output capacitance is also of interest
primarily because it affects high frequency
performance. Besides measuring junction capacitance
with a bridge, output admittance measurements are
sometimes made at various frequencies from which most
high-frequency-limiting factors may be deduced.
Admittance and impedance bridges are offered for these
kinds of measurements that perform well beyond 1 GHz.

HIQ-l- FREQUENCY CURRENT GAIN
As with the measurement of input and output
admittance at high frequencies, measurement of
transfer functions at high frequencies can be made
with bridges designed for that purpose.

f hfe -- Cut-Off Frequency for h fe
The small-signal current transfer ratio for
transistors operated in the common-emitter mode
invariably becomes smaller and smaller at higher
and higher frequencies. The frequency at which the

55

current gain of a transistor driving a low impedance
load decreases by 3 decibels (current down 29.3%) is
the cut-off frequency. For example, a transistor
having a current gain of 100 at low frequencies would
have a current gain very close to 70 at the cut-off
frequency. There would still be a very considerable
gain at the so called "cut-off" frequency.

f

f T - no gain

gain
bandwidth
product

T

-- Frequency of Unity Current

Gain~

Common-Emitter

As the small-signal short-circuit current gain of a
transistor is measured for signals having higher
frequencies than fhfe' a frequency can be found where
the gain has diminished to unity, or one. At higher
frequencies than that the current gain is less than
one, that is, a loss. So fT can be considered the
frequency beyond which the transistor will not
provide current gain.
The frequency fT can usually be determined using
equipment that does not extend to fT in direct
frequency measurement capabilities. The reason is
that current gain usually falls off at the rate of 6
db (50%) every time the frequency is doubled, beyond
the cut-off frequency. The roll-off curve is usually
very similar to a simple RC curve. From such a curve
fT may be extrapolated. Usually a checkpoint or two
is selected at one or two frequencies beyond the
cut-off frequency to assure a more reliable
calculation. The symbol fT is sometimes called the
gain-bandwidth-product frequency, because the
product of gain and frequency will be a constant
for frequencies beyond fT and fairly constant for an
octave or two below fT when hfe is high at low
frequencies.
f

hfb

-- Common-Base Cut-Off Frequency

The common-base mode does not provide a current gain.
Gain is typically very close to one but never is
more than one. Nonetheless, even this low gain
falls off at high frequencies. The frequency at
which the gain falls 3 db below that for low
frequencies and DC is fhfb. This cut-off frequency
is usually in the same vicinity as fT'

56

INPUT IMPEDANCE

bipolar
transistors
have low
Z input

Z input hiehibhic
- R input

R input
non I i near

Bipolar transistors are current-controlled
semiconductor devices, and have low input resistance
compared to vacuum tubes and field-effect transistors.
To calculate the loading effect that a transistor
will present to whatever driving source it may be
connected to requires a knowledge of its input
characteristics. Except at high frequencies where
input capacitance may influence input impedance, and
except for extremely high frequencies where
transistor lead inductance may enter the picture, the
input characteristics of a bipolar transistor are
essentially resistive in nature. Measurement of h. ,
h ib , and h. -- the small-signal h-parameter commofi~
emitter, c5~on-base, and common-collector symbols
for input impedance -- pertain strictly to resistance,
because they apply at only low frequencies and DC.
Input resistance is, however, typically nonlinear if
measured over a wide range of driving current.
It is because of the nonlinear nature of input
resistance that we must be specific about the
conditions for measuring it. Any transistor can be
operated in a variety of ways to have a wide range
of input resistance values. The common-collector
mode offers the highest input impedance by quite a
margin, extending into megohms, when the load is also
a high impedance. The common-base and common-emitter
modes have low input impedance values. This range may
be from a fraction of an ohm to over 1000 ohms
depending on the amount of forward bias, and whether
tl~ collector voltage is near saturation.
The
common-base configuration has the lowest input
impedance by a considerable margin, for comparable
amounts of collector current.
hIE and hie -- Static and Dynamic Input Resistance~

Common-Emitter.
Static input resistance, hIE' is equal to the quotient
of the voltage-drop across the base-emitter terminals
and the base current producing that voltage drop -- at
a given collector voltage. It can be easily
calculated after the current and voltage have been
measured with simple DC instruments. Or the currents
may be applied and voltages read from the curves
presented by a transistor curve tracer. See Fig. 1-29.

57

POINT A

B

.32

IB
.25mA
.20mA

.28

.15mA

t

VBE
( V)

.24

.10mA

.20

·.05mA

.16

.12

2

0

3

VeE (VOLTS)

+/

5

4
~

+rrm
0

0

CURRENT
STEPS

VOLTAGE
SWEEPS

B

E

Fig. 1-29.

Input resistance, 2N1304. Five
constant current base steps applied.
Voltage between base and emitter
terminal 20 mV/div -- offset 120 mV.
Dynamic input resistance (hie)
between point A and point B = 20 mV
(6VBE) divided by .05 rnA (6IB) which
equals 400S"l.

58

h.Ie

From the same display one may also determine dynamic
(differential) input resistance, hie' The symbol hie
stands for dynamic input resistance measured with
the output load essentially zero ohms. The term
"small-signal short-circuit" implies that the
collector voltage should remain constant when the base
current is changed. When measured on a curve tracer
therefore, a vertical line at any horizontal position
corresponds to one particular collector voltage. The
vertical distance between curves at the horizontal
position corresponding to a given collector voltage
is proportional to the change in voltage drop at the
base induced by a selected change in base current.
Dividing the measured change in base voltage, 6VBE ,
by the selected change in base current, 6I B , gives
the differential input resistance for that set of
conditions.
By looking at the set of curves and noting the
difference in vertical distance between each of them
you can instantly perceive the difference in input
impedance at various bias conditions. The vertical
distance between adjacent curves is directly
proportional to the dynamic input resistance at any
given collector voltage.
h

and h

IB
ib
Common-Base

-- Static and Dynamic Input

Resistance~

Static input resistance, h IB , is equal to the
quotient of the voltage drop across the emitter-base
terminals and the emitter current. The collector
voltage will have a small influence so it should be
specified.

measure hiE
and hFE,
calculate
hiS

The voltage-drop across the emitter-base terminals is
due to base current, the same as for the commonemitter mode, not due to emitter current. Therefore,
if we were to start with the same amount of base
current as we did for a measurement of input
impedance in the common-emitter mode, we can compare
input impedances of two modes. Under these
conditions we would compare the quotient of VBE/I B
with the quotient of VBE/IE' This is like simply
comparing base current (IB) with emitter current (IE)'
In other words, input resistance for the common-base
mode is much less than for the common-emitter mode,
when other conditions are the same.

59

So h IB may be determined by measuring hIE and
then calculating h IB .

hFE ,

hIe and h ic -- Static and Dynamic Input Resistance,
Common-Collector
The input impedance for the common-collector
configuration is higher than the common-emitter
configuration, except when the load is zero ohms.
When the load is zero ohms the input resistance is
the same as for the common-emitter mode. Therefore,
hIe and h ic ' which are symbols for static and
dynamic input resistance with output short-circuited,
can be measured using the common-emitter configuration.

Input Impedance of Emitter-Followers

emitter
output
fo I lows base
input

operati ng
limits

The load, in the common-collector mode, is driven by
the emitter rather than the collector. The circuit
configuration is frequently called an emitterfollower, unless the load is close to zero ohms.
Emitter-followers are seldom intended to drive zero
ohms, so in practice, the input resistance is higher
than for the common-emitter mode.
The voltage at
the emitter terminal, because it must remain close
to the voltage at the base terminal except when the
transistor is cut off, will move up and down closely
following the voltage excursions on the base. As
long as the voltage excursions don't go beyond the
voltage level to which the emitter load is returned,
where cutoff or breakdown would occur, or too close
to the level of the collector supply voltage, where
saturation would occur, an emitter follower may be
made to operate normally.
When the load driven by an emitter follower is high
compared to the input resistance of the same
transistor operated in the common-emitter mode, the
input resistance is approximately equal to the
product of the resistance of the load (R L ) and the
common-emitter forward current transfer ratio (h FE ).
The static value of input resistance differs somewhat
from the simple product of h FE and RL because the
collector-to-emitter voltage does not remain

60

constant as collector current changes in an emitterfollower. When current increases in an emitterfollower, the emitter voltage approaches the
collector voltage and thereby reduces the current
transfer. Likewise when base current is reduced and
collector current is also thereby reduced, the
collector-to-emitter voltage increases. The net
increase in collector voltage retards the reduction
in emitter current.

20 ~A/step
x 6 steps

The combined effect can readily be discerned and
measured on a transistor curve tracer by connecting
the selected value of load resistance between the
emitter terminal and ground then displaying a family
of curves depicting collector current versus collector
voltage. See Fig. 1-30. At a collector-to-ground
voltage of 5 volts, 4 rnA of collector current flows
when base current is 0.12 rnA (6 x .02 rnA). The
static input resistance at this point (Point A) on
the curve would be equal to the base-to-ground voltage
divided by the base current. The base current
(0.12 rnA) plus the collector current (4 rnA) flows
through RL producing 4.12 volts of drop. So the base
voltage will be close to 4.12 volts. Actually it will
be about 0.6 volts more than that because the baseemitter junction is forward biased. The static input
impedance is, therefore:
4.72 volts
.00012 amperes

40,000 ohms

This operating point is very close to saturation, as
can be seen by the knee on the curve just below the
5-volt collector voltage point on the curve. This
transistor would not normally be operated as an
emitter follower with more than 4 volts on the base
unless it were operated with a higher collector
voltage than 5 volts.
The differential input resistance would depend on how
the transistor was biased in the quiescent condition
and how big the changes of input voltage are. If we
consider the quiescent condition to be with .06 rnA of
base current and 5 volts on the collector, the midsection of the middle curve (Point C) in Fig. 1-30 is
representative. Collector current is 1.7 rnA and base
current .06 rnA, so emitter current is 1.76 rnA. This
means an emitter voltage of 1.76 volts (voltage drop
across 1 kilohm) and a base voltage very close to 0.6
volts higher than that, or 2.36 volts. If we raise

61

ABC
5

4

3

2

o

o

2

4
V

c

Fig. 1-30.

differential
input R
6V

H

B

B

6

8

10

(VOLTS)

2N3l37 emitter follower conductance
characteristics. RL equals 1000~.
Base current steps are 20 ~.

the base-to-ground voltage enough to increase base
current from .06 rnA to .08 rnA (Point B), collector
current will increase from 1.7 rnA to 2.4 rnA, a change
of 0.7 rnA.
Emitter current will change from 1.76 rnA
to 2.48 rnA, a change of 0.72 rnA.
If we assume that
the base-emitter forward voltage drop remains
essentially constant, which it does except near
cutoff, the change in emitter voltage is a good
measure of the change in base terminal voltage. The
change in emitter voltage is proportional to the
change in emitter current and is equal to the product
of the load resistor, 1 kilohm, and the emitter
current change, 0.72 rnA. This product equals 0.72
volts.
The differential input resistance is equal to
a change in base-to-ground voltage divided by the
accompanying change in base current.
By applying a
known base current increase and calculating the base
voltage increase, the differential input resistance
is determined.
In the example the dynamic input
resistance is:

0.72 volts
.00002 amperes

36,000 ohms

62

The same measurement can be performed when reducing
input voltage and current as when increasing input
voltage and current. The vertical separation between
the curves at a particular co11ector-to-ground
voltage is proportional to the differential input
resistance.

OUTPUT AnVlITTANCE
Admittance is the reciprocal of impedance so
measurements of output admittance are similar to
measurements of output impedance. A high impedance
is the same as a low admittance. Impedance is
equal to voltage divided by current so admittance
is equal to current divided by voltage.

hoe -- Dynamic Output

Admittance~

Common-Emitter

The output admittance, or output impedance, of a
transistor tells us what effect on current through
the transistor a change in the output terminal
voltage may cause. Measurement of a transistor's
output admittance is usually done by simulating a
constant-current or "open-circuit" input.
Transistor curve tracers simulate this condition
very well.

slope above
knees for
Z
or Y
out
out

Any curve which is a plot of current versus voltage
has a slope which is equivalent to some impedance
and some corresponding admittance. The collector
current versus collector voltage curves that
represent different discrete values of base current
have two principal slopes. The slopes below the
knees represent saturation resistance. Above the
knees of the curves, the slopes represent output
admittance or output impedance. The more nearly
horizontal a section of a curve is, the less will be
the output admittance it represents, provided
current is plotted on the vertical axis and voltage
is plotted on the horizontal axis. Most curves on
most transistor curve tracers depict current on the
vertical axis.
Small-signal output admittance for the commonemitter mode is measured at a given base current and
between two given collector voltages. The difference
in collector current that would accompany the change

63

in collector voltage represented by the difference
between two given collector voltages is proportional
to output admittance. For the common emitter mode:

h

when base current is kept constant.

oe

See Fig. 1-31.

POINT A

POINT B

10

8
6
4
2

o
o

.4

.8

1.2

VeE (VOLTS)

CURRENT
STEPS

Fig. 1-31.

B

1.6

..

2.0

VOLTAGE
SWEEPS

Output admittance (hoe) depends on
slope of curves. ~VC and ~IC
between point A and point B determine
output admittance for base current of
250 ]..IA.

64

When the slope of a curve is nearly horizontal,
expanding the display vertically so only a portion
remains on screen will accentuate the slope and
permit more accurate measurements to be made.
See
Fig. 1-32.

PO I NT B

POINT A

7.0
C
(mA)
6.8
I

6.6

o

.4

.8

1.2

VCE (VOLTS)

CURRENT
STEPS

B

1.6

2.0
~

VOLTAGE
SWEEPS
E

Fig. 1-32.

Output admittance measurement
accuracy improved with lOX vertical
magnification. 6IC = .18 rnA;
6VCE=lV.

65

hob -- Dynamic Output Admittance, Common-Base
The measurement of the output admittance of a
transistor operated in the common-base configuration
is done in very much the same way as for the commonemitter configuration. The common-base mode has a
lower output admittance than the common~co11ector mode
or the common-emitter mode. It follows that the
output impedance for the common-base mode is the
highest of the three modes. The slope of the curves
which represent graphs of collector current versus
collector voltage for various discrete amounts of
emitter current is very nearly horizontal, as can be
seen in Fig. 1-33. Compare Fig. 1-33 with Fig. 1-34.

POINT A

POINT B

20

i

I

16
12

C 8

(rnA)

4
0

-1

2

0
V
CB

4

3

(VOLTS)
+

o

o~
CURRENT
STEPS

Fig. 1-33.

5

s----"<:::::.../
I--_..

rvvY\

VOLTAGE

SWEEPS

Output admittance (hob) depends on
slope of curves. See Fig. 1-34.

66

POINT B

POINT A

19.8

t

IC

(mA)

19.4
19.0
18.6
18.2

-1

0

1

2

3

4

5

~

V
(VOLTS)
CB

+rvrn

0

:~
CURRENT
STEPS

Fig. 1-34.

B

VOLTAGE
SWEEPS

Output admittance (hob)'
.08 rnA; 6VCB = 3 V.

6IC

67

Output admittance is the quotient of a collector
voltage change and an accompanying collector current
change at some region out of saturation. Usually
emitter current is held constant. For the common-base
mode:

when emitter current is kept constant.

hoc -- Dynamic Output

Admittance~

Common-Collector

The measurement of hoc is made by measuring hoe for
equivalent conditions and considering the two equal.

REVERSE VOLTAGE TRANSFER

watch it!

Reverse-voltage transfer is a little like forwardcurrent transfer; each is expressed as a ratio of a
change at an output terminal compared to an
accompanying change at an input terminal.
Unlike
forward current transfer, where the change in the
output current is naturally considered a result of
a change in the input current, reverse voltage
transfer is the opposite. A change in output
voltage can be considered to cause a change in input
voltage when input current is held nearly constant.
The reverse voltage transfer characteristic is
important because a change in current through a
transistor does often cause a considerable change
in voltage at the output terminal, depending on the
load, and this voltage change may affect the
operation of the transistor.
The measurement of the small signal reverse voltage
transfer parameters hr ,h
and h
requires the
.
e
rh
Th lS
. rc con d"ltlon lS
.
lnput
current to b e constant.
comparable to the current being supplied through a
very high resistance -- ideally an infinite resistance
or "open-circuit."

h re -- Reverse Voltage

Transfer~

Common-Emitter

Measurement of the reverse voltage transfer ratio
for the common-emitter mode using a transistor curve
tracer may be accomplished by plotting base voltage
versus collector voltage for various discrete base
currents. The slope of the curves any place beyond
the knees will be an indication of the reverse
voltage transfer ratio. The measurement is made by

68

POINT B

POINT A

IB
.30

.25mA

.26

r

VBE

.22

( V)

.18

.14

o

123

4

5

VeE (VOLTS)

Fig. 1-35.

Reverse voltage transfer (h re )
2N1304, at base current of .25 mAo
6VCE between point A and point B is
4 volts. 6VBE between same points is
. t e 1y 4 m.
V
approxlma

1

1000'

hre = ~
.004V

69

first finding the appropriate points on the
appropriate curve that constitute the difference in
collector voltage required, then measuring the
difference in base-emitter voltage drop that
corresponds to those points on the curve. Dividing
the collector voltage difference (6VC) by the base
voltage difference (6V BE ) yields the transfer ratio.
See Fig. 1-35.

h

rb

-- Reverse Voltage

Transfer~

Common-Base

The measurement h rb can be made in a way similar to
measuring h re , but the accuracy will be even less
because the curves will be more nearly horizontal.

h

rc

-- Reverse Voltage

Transfer~

Common-Collector

The reverse voltage transfer ratio for the commoncollector mode is typically very close to one (1)
because hre is typically a very small fraction.

hrc =

1 -

hre

71

FIELD EFFECT TRANSISTORS

LEAKAGE AND BREAKDOWN

I GSS and V(BR)GSS -- Leakage