September 1969 Electronics World
Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
Electronics World, published May 1959
- December 1971. All copyrights hereby acknowledged.
Like most people familiar with electronics, when negative resistance semiconductors are mentioned,
I immediately think of tunnel diodes. Negative resistance is the characteristic where in increase
in voltage across the p-n junctions results an a decreased current. Although the tunnel diode
was invented by by Leo Esaki (Sony) in 1957, it is not mentioned anywhere in this 1969 article.
Instead author Wesley Vincent (Motorola) describes the theoretical operation of 4-layer (3
junction) semiconductors and how they can be biased to mimic true negative resistance devices.
Given that one of the most common applications of tunnel diodes is to construct relaxation
oscillators, knowing which configurations of standard BJTs can act like negative resistance
devices might help explain unintended high frequency oscillations in some amplifier circuits.
Using Transistors as Negative-Resistance Devices
By Wesley A. Vincent / Advanced Development Section
Government Electronics Div., Motorola Inc.
By using simple transistor-resistor combinations, characteristics
of four-layer diodes, SCR's, and UJT's may be readily simulated.
Several rather unusual negative-resistance devices have become available to the circuit
enthusiast during the past few years. These devices include four-layer diodes, silicon controlled
rectifiers (SCR's), and unijunction transistors (UJT's) to name a few of the most popular.
Industrial competition and improved manufacturing and production techniques have resulted
in price reductions, allowing those with limited budgets to use them in circuit projects.
However, ordinary transistors are more likely to be readily available for circuit experiments.
By using the simple transistor-resistor combinations presented in this article, the characteristics
of four-layer diodes, SCR's, and UJT's may be simulated.
A relaxation oscillator using the analog circuit of the unijunction transistor, which is
quite similar in operation to the unijunction relaxation oscillator, is also described. Although
the test results presented were obtained using silicon transistors, low-leakage germanium
transistors may be substituted.
An advantage gained in simulating these negative-resistance devices is that the more important
device parameters may be determined by selecting transistors and resistors used in the substitute
combinations. The basic building block for the circuits discussed is based on the operation
and theory of the four-layer or p-n-p-n diode. The SCR and UJT are then presented as extensions
of the four-layer diode in theory and in synthesizing their characteristics, using transistor-resistor
Four-Layer Diode Theory
A four-layer diode consists of four alternate regions of p- and n-doped semiconductor,
as shown in Fig. 1A. The p-region terminal is called the anode while the n-terminal is referred
to as the cathode. The V-I characteristics and parameter definitions associated with the device
are shown in Fig. 1B. With the anode biased positively with respect to the cathode, a negative-resistance
(current increases as the voltage decreases) region exists. The four-layer diode may also
be represented by a regenerative transistor feedback arrangement consisting of a p-n-p and
n-p-n transistor, as shown in Fig. 1C.
Using this model, the mathematical expression for the terminal current IE, may
be expressed in terms of the transistor parameters as follows:
and αn are
the common-base current gains; Icop and Icon are the collector-to-base
leakage currents; Mp and Mn are the multiplication factors which account
for carriers created by impact ionization in a reverse-biased junction during breakdown.
Fig. 1A - Four-layer diode has four alternate "p, n" regions and three
"p-n" junctions. B - V-I characteristics
Fig. 1C - Transistor model
The p and n subscripts refer to the parameters associated with the p-n-p and n-p-n transistors,
respectively, in Fig. 1C. Usually Mp and Mn are assumed to be equal
and are designated simply as M. If the leakage terms are combined, the previous equation may
be expressed in a slightly more simplified form as:
This expression may be used to briefly explain the forward V-I characteristics of the four-layer
diode as follows: For anode-to-cathode voltage less than the breakover voltage, only a small
leakage current flows. The current-gain parameters
αn are complex
functions of injection efficiency, the base transport factor, and surface conditions. For
small anode-to-cathode voltages, the combined values of
αn are much
less than 1. Since no multiplication takes place at low voltages, M is equal to unity. The
denominator in the above expression is only slightly less than unity so that IE
is approximately equal to Ico.
The current gains αp
and αn increase
with increasing current as the forward voltage is increased. Thus, the forward current increases
slightly with increasing voltage. As the forward voltage is continually increased, the condition
occurs where M (αp
+ αn ) =
1. When this occurs, the current increases sharply over the previous small leakage current
as shown in Fig. 1B. This voltage is known as the breakover voltage. At the breakover voltage,
multiplication (M) is greater than unity since avalanche breakdown is occurring in the reverse-bias
junctions. Therefore, the combined value of
αn is less
As the current increases beyond the breakover current,
due to their current dependence. A lower multiplication (M) is then required to maintain the
breakover voltage. As a result, the forward bias across the diode begins to decrease with
a negative-resistance region occurring. The current increases and voltage decreases until
the holes injected at the anode of the p-n-p transistor equal the electrons injected at the
emitter of the n-p-n transistor. This is a result of current continuity conditions and results
in forward bias of the center junction of the four-layer diode. The transistors in the model
are then in their "on" or saturated state.
In the reverse operating mode, the four-layer diode acts like two reverse-biased diodes
in series. A small reverse current exists until the breakdown condition finally takes place.
Equivalent Circuit for Four-Layer Diode
When silicon transistors are connected in the manner shown in Fig. 1C, the forward V-I
characteristics resemble those of an ordinary p-n junction rather than those of a four-layer
diode. This occurs because the discrete transistor current gains are much higher than the
current gains in a four-layer diode. The breakover condition of M (αp +
αn) = 1 is
reached at a few tenths of a volt when current injection for the transistor begins.
Large transistor leakage currents can also cause low breakover voltages. One method of
reducing the transistor current gain is to place a resistor between its base and emitter terminals.
A shunt path exists for the emitter current with the result that very little injection takes
place until the voltage across the shunt resistor begins to forward-bias the base-emitter
In the transistor equivalent model shown in Fig. 1C, several possibilities exist for reducing
the combined values of αp
and αn. Resistors
can be inserted between the base and emitter of the p-n-p or n-p-n, or both, transistors.
Shown in Figs, 2A and 2B are the forward V-I characteristics for a transistor-resistor equivalent
circuit with a 1000-ohm resistor inserted between the base and emitter of the n-p-n transistor.
It can be seen from these curve-tracer photographs that the forward V-I characteristics are
similar to those of the four-layer diode.
Fig. 2 - (A, B) The transistor-resistor equivalent circuit for a four-layer
diode. (C) Same but with inverted "n-p-n" transistor and (D) with an inverted "p-n-p" transistor.
In the configurations shown, the breakover voltage is determined by the BVCEO
parameter of the p-n-p transistor. In general, the breakover voltage will be determined by
the transistor with the lower breakdown parameter. Shunt resistors, used to reduce either
increase the transistor breakdown voltage from BVCEO to BVCER. In Figs.
2A and 2B, BVCEO for the n-p-n transistor is approximately 50 V. However, with
the shunt resistor of 1000 ohms, the BVCER voltage is greater than 100 volts; hence,
the breakover voltage for the circuit is determined by the p-n-p transistors with BVCEO
voltages of 54 and 64 volts, respectively.
For breakover voltages less than the BVCEO voltage of the transistors, either
the p-n-p or n-p-n transistor may be operated in an inverted mode. Results for such a circuit
are shown in Fig. 2C where the n-p-n transistor has been inverted. Even though alpha for an
inverted transistor is severely reduced, it is still necessary to reduce the alpha of either
the n-p-n or p-n-p transistor with a shunt resistor. As with the previous circuit, the breakover
voltage is determined by the lower breakdown of the two devices. In this configuration the
breakover point is determined by the BVECO voltage of the n-p-n transistor. (A
close approximation of the breakover voltage is obtained by knowing the more commonly specified
BVEBO voltage of the n-p-n transistor.)
Another four-layer diode equivalent circuit with its forward V-I characteristics is shown
in Fig. 2D, where the p-n-p transistor has been inverted. The BVECO voltage of
the p-n-p transistor determining the breakover voltage is 6.5 volts.
By selecting the transistor breakdown voltage, the experimenter can simulate four-layer
diode characteristics with a breakover voltage of 5 to 100 volts or more.
The holding current for these configurations is determined by the transistor current gains
and shunt resistors. The holding current may be selected from a few microamps to 10 or 20
mA or more. Decreasing the value of the shunt resistor (and hence decreasing the transistor
current gain) increases the holding current.
The reverse breakdown voltage for the four-layer diode equivalent circuit is similar to
that of a four-layer diode and is determined by the junction breakdown of the transistors
in the specific configuration. Note that if shunt resistors are used to reduce both
αn, the reverse
breakdown voltage will be only approximately 0.65 volt, the voltage of one forward-biased
The most noticeable temperature effect for these configurations is that the holding current
decreases with increasing temperature. If the transistor alphas are not reduced sufficiently
by shunt resistors, it is possible for premature firing to occur with increasing temperature
as αp and
The test results are not unique for any particular transistor type. Similar results have
been obtained using other silicon and low-leakage germanium transistors.
Simulation of SCR Characteristics
Fig. 3. (A) An SCR is four-layer diode with gate terminal. (B) V-I characteristics,
and (C) equivalent circuit for SCR.
Fig. 4. Characteristics of simulated SCR shown here (A) in blocking state
and (B) in "on" state due to 1 V on gate.
Fig. 5. (A) Symbol and circuit used to explain operation of UJT. (B) Forward
V-I characteristics. (C) Equivalent circuit.
The SCR consists basically of a four-layer diode with the addition of a third terminal
called the gate. The gate is usually attached to the p-region near the cathode, as shown in
Fig. 3A. The gate terminal is used to switch the SCR from the blocking or "off" state to a
low-impedance or "on" state . As the gate current increases, the breakover voltage decreases,
as shown in Fig. 3B.
With a minimum gate current, which is dependent on the particular SCR construction, the
negative-resistance region no longer occurs and the V-I characteristics resemble those of
an ordinary p-n diode. In theory, the gate current causes the individual current gains
αn to increase
so that the condition for breakover, M (αp +
αn) = 1,
occurs prior to four-layer junction breakdown.
The transistor-resistor equivalent circuit for the four-layer diode may be adapted to obtain
SCR characteristics by simply adding the gate terminal with a series resistor to the base
of the n-p-n transistor shown in Fig. 3C. The series gate resistor insures that the collector
current of Q1 causes Q2 to turn on, leading to regenerative action and the low-impedance state.
Otherwise the collector current (electron current) of Q1 would flow into the gate terminal.
A diode may also be used to replace the series gate resistor in Fig. 3C.
Curve-tracer results for the simulated SCR are shown in Fig. 4, where Q1 and Q2 were 2N3906
and 2N3904, respectively. Both resistors used in the equivalent circuit were 1000 ohms.
Fig. 4B shows the equivalent SCR turned "on" by an applied gate voltage of 1 volt. The
exact gate voltage and current necessary for switching the simulated SCR will depend on the
transistors and resistors used in the equivalent circuit. A gate current of 1 milliamp should
be sufficient to switch silicon or germanium combinations.
Simulation of the Unijunction Transistor
The unijunction transistor is another device with negative-resistance characteristics.
It is used in oscillators, timing circuits, pulse and sawtooth generators, and special triggering
applications. The unijunction equivalent circuit can be considered to be a resistive n-type
silicon bar with a p-n junction formed between the terminals, as shown in Fig. 5A. The end
terminals of the bar are referred to as bases while the anode of the p-n junction is called
the emitter. The resistance between the two bases is known as the interbase resistance. The
geometry of the first unijunctions consisted of the bar structure although newer UJT's include
cube, planar, and p-base complementary structures.
In operation, the interbase resistors form a voltage divider with the voltage applied between
base terminals. When the voltage at the emitter forward-biases the p-n junction, the unijunction
enters the negative-resistance region. Forward V-I characteristics for the unijunction, showing
the negative-resistance region, are illustrated in Fig. 5B.
The unijunction transistor can be considered to be a four-layer diode with the addition
of biasing resistors as shown in Fig. 5C. The biasing resistors replace the interbase resistors
of the unijunction and are used to set the break over point. However, in unijunction terminology,
this voltage is known as the peak-point voltage. Also, the minimum holding current is referred
to as the valley current (IV) for the unijunction.
For commercially available UJT's, the ratio of interbase resistors setting the peak-point
voltage is determined by the semiconductor manufacturer. Using the transistor-resistor equivalent
circuit in Fig. 5C, the peak-point voltage may be selected by choosing the appropriate resistive
dividers, RI and R2.
Fig. 6. (A) UJT oscillator. (B) Equivalent-circuit version.
A relaxation oscillator is one of the most common applications for the UJT. The basic configuration
appears in Fig. 6A. A positive pulse appears at base 1, a negative pulse at base 2, and a
sawtooth waveform at the emitter. The frequency of oscillation is controlled by the R1C1 time
constant; R2 is selected for minimum frequency change over a given temperature range, and
R3 limits the capacitor discharge current.
The basic operation of the relaxation oscillator is as follows: When "B+" is applied, all
of this voltage immediately appears across the timing resistor, R1. The voltage across C1
then increases at a rate determined by the time constant R1C1 as C1 begins to charge toward
the applied voltage. When the voltage across the capacitor increases to the emitter firing
voltage, the emitter-base 1 junction becomes forward-biased and the UJT enters the negative-resistance
region. C1 then discharges through R3 and the emitter of the unijunction, this continues until
the voltage across C1 falls sufficiently and causes the UJT to turn off. When the UJT turns
off, the applied voltage minus the turn-off voltage appears across R1. The capacitor begins
to charge again and the cycle is repeated. Positive and negative output pulses are produced,
as shown on the diagram, as a result of the pulse of current flow through the UJT. During
firing, negative resistance occurs between the emitter and base 1 due to carriers injected
across the junction. This mechanism is known as conductivity modulation of the bulk silicon.
The configuration of the equivalent-circuit relaxation oscillator and its similarity to
the UJT oscillator are shown in Fig. 6B. The operation is similar to the unijunction oscillator
except that the capacitor is discharged through the low impedance, resulting from the four-layer
action of Q1 and Q2 when firing occurs. Component values in Fig. 6B are for an oscillator
with a frequency of approximately 1 kHz.
The firing point for this circuit is:
or approximately 5.5 + 0.6 = 6.1 volts. A positive pulse can be obtained by dividing R2
into two separate resistors and taking the output between them.
In summary then, we have shown that it is possible to simulate the characteristics of four-layer
diodes, SCR's, and UJTs by simply wiring together a pair of transistors and some resistors.
Posted July 3, 2017