July 1963 Electronics World
Table of Contents
People old and young
enjoy waxing nostalgic about and learning some of the history of early electronics. Electronics World
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Most RF Cafe visitors are familiar with the negative
resistance region exhibited in tunnel diodes. It is what makes them usable, among other special applications,
as oscillators. Although a diode is often part of an AC circuit, it is fundamentally thought of as a
DC device since it permits conduction in only one direction (the exception being a Zener diode). An
AC device in general refers to something used in a line supply circuit at 50 Hz, 60 Hz, or
even 400 Hz. Such is the case with this article, which describes negative resistance characteristics
of voltagevariable capacitors (varactor) and ferroresonant devices like saturable coils.
See author's "Negative Resistance: What
It Is & How It's Used" article in the May 1961 Electronics World.
A.C. NegativeResistance Devices
Description of ferroresonators, nonlineartype capacitors, semiconductor capacitors, and other similar
components.
By Rufus P. Turner
Fig. 1. Basic curves of the a.c. negativeresistance devices discussed below.
The author's earlier article on negative resistance was devoted to directcurrent devices.^{1}
However, that article stated in conclusion that certain a.c. devices also exhibit the property of negative
resistance, or negative impedance. This article describes devices of this type.
For simplicity's sake, throughout this article the term "negative resistance" will be used in a generic
sense. But the reader will recognize that the negative quantity may be impedance or reactance, rather
than resistance.
Such a.c. negativeresistance devices are not nearly as numerous as the d.c. devices, but we may
reasonably expect additions to the family as research and development continue. The external manifestations
of a negative characteristic are substantially the same in a.c. and d.c. devices, that is, the conduction
curve has a negative slope over some part of it. In one instance, current will be the independent variable;
in another, voltage will be. Thus in Fig. 1A, current is the independent variable. As the a.c. current
is continuously increased, the a.c. voltage drop across the device first increases from 0 to A and then
decreases (showing a negative resistance) from A to B. In Fig. 1B, voltage is the independent variable.
As the applied a.c. voltage is continuously increased, the a.c. current flowing through the device first
increases from 0 to A, and then decreases (showing negative resistance) from A to B.
The following sections describe the action of devices which exhibit one or the other of these conduction
characteristics.
Ferroresonator
Fig. 2. (A) Basic ferroresonant circuit arrangement. (B) Test circuit showing operation
of the ferroresonant element. (C) Graph of operational characteristic.
The ferroresonator (also called "ferroresonant circuit," saturablereactor switch," and "ferristor")
is a special type of seriesresonant LC circuit. It really is quite simple, consisting only of a coil
and capacitor connected in series (see Fig. 2A). The capacitor is a conventional one but the coil is
not. The special feature of the coil is its core which saturates readily. Because of core saturation,
the inductance and reactance of the coil decreases as the current is increased. An ordinary ironcore
filter choke will exhibit saturation and a resulting decrease in inductance if current is raised high
enough, but this usually requires a rather large current at powerline frequencies. A ferroresonator
coil intended for operation between 100 kc. and several megacycles, however, is wound on a tiny, thin
core of highpermeability metal and will saturate on only a few milliamperes.
The LC combination resonates at a frequency, f_{r}, determined by the inductance and capacitance
values. (Resonant frequency . Capacitance C is constant, but inductance
L varies with the current, I, flowing through the circuit, so the resonant frequency changes with current.
(As I increases, L decreases, and f_{r} increases.) This is the basis of Ferroresonator operation.
Fig. 2B shows a typical ferroresonant circuit. Here resistance R is noninductive. The generator
provides an adjustable a.c. output voltage. By adjusting the voltage, the operator varies current I
flowing through R, L, C in series. The voltage (E_{LC}) across the LC combination is measured
with a highimpedance a.c. vacuumtube voltmeter. Fig. 2C shows circuit response. As the current is
steadily increased, voltage E_{LC} rises to a peak (point A), then decreases to a valley (point
B), and finally rises again to C and beyond. Thus, AB is a negativeresistance region bounded by two
positiveresistance regions (0A and BC). This is a typical negativeresistance curve.
The circuit behavior may be explained in the following manner. (1) The L and C values are selected
to give a resonant frequency somewhat lower than the generator frequency. Increasing the current decreases
inductance L and tunes the circuit up to the generator frequency and finally to some still higher frequency.
(2) As I is increased from zero, E_{LC} rises and would continue to do so if the core of the
coil did not begin to saturate. Saturation (starting at point A in Fig. 2C) lowers the inductance and
tunes the circuit toward resonance at the generator frequency. (3) At generator resonance, the net reactance
of the LC combination is theoretically zero, therefore E_{LC} is theoretically zero. As
resonance is approached, E_{LC} accordingly decreases. At resonance (point B), E_{LC}
does not drop fully to zero because resistance losses remain to act in the circuit after resonant cancellation
of the reactance. (4) As I is increased further, core saturation increases, inductance lowers still
more, and the circuit is tuned to a frequency higher than the resonant frequency. Thus, the voltage
once more rises  in this case from B to C.
Tiny r.f. ferroresonators have been used as active elements in flipflops, electronic counters, gates,
and other computertype devices.^{2,3,4} They also have been employed as magnetic amplifiers
at audio frequencies. In these particular units, C usually is a fairly small mica capacitor, while L
is a coil that has been wound on a core of Permalloy foil.
Nonlinear Capacitor Element
Fig. 3. (A) Basic circuit arrangement using a nonlinear capacitor. (B) Test circuit showing operation
of the nonlinear element. (C) Response of the test circuit.
Fig. 4. Alternative circuit with a semiconductor capacitor.
Fig. 3A shows a seriesresonant negativeresistance circuit which resembles the ferroresonant circuit
described in the preceding section but behaves somewhat differently. This arrangement uses a conventional
aircore coil and a nonlinear (voltagevariable) capacitor. Suitable capacitors of this type contain
a highK ceramic dielectric, such as specially processed singlecrystal barium titanate. As the voltage
applied to the capacitor is increased, the capacitance decreases.
As in the standard ferroresonant circuit, the L and C values in Fig. 3B are selected so that the
zerovoltage resonant frequency of the circuit is lower than the generator frequency. As the voltage
is increased, the current rises from zero to a peak point (A in Fig. 3C). As the voltage is increased
further, the current decreases. Thus, the currentvoltage curve has a negative slope from A to B.
Behavior of the circuit may be explained in this manner. (1) The increasing voltage lowers the capacitance
and tunes the LC circuit up toward the resonant frequency (generator). The current increases because
increasing capacitive reactance causes the net reactance of the circuit to decrease. (2) At resonance
with the generator, the net reactance is theoretically zero, and maximum current flows. This corresponds
to point A in Fig. 3C. (3) As the voltage is increased beyond this point, the circuit is tuned to frequencies
higher than resonance. The capacitance continues to fall but the net reactance of the circuit increases,
so the current decreases. This is represented by the negative slope, AB.
Semiconductor Capacitor Circuit
A ceramic nonlinear capacitor, such as C in Fig. 3, usually requires relatively highvoltage operation
for appreciable capacitance change. Furthermore, such capacitors are quite temperaturesensitive because
of the Curie point of the dielectric material. To obtain lowvoltage operation (from a few tenths of
a volt to 1 to 6 volts r.m.s.) and at the same time to secure comparative freedom from temperature effects,
semiconductor voltagevariable capacitors may be substituted in the circuit, as shown in Fig. 4. Response
is the same as that shown in Fig. 3C.
In Fig. 4, the semiconductor voltagevariable capacitor (also known as Varicap, varactor, Semicap,
etc.) is d.c.biased in a reverse direction to set its initial capacitance to a desired value and to
prevent positive peaks of the maximum r.f. voltage from driving the semiconductor junction into the
lowresistance forward direction. C1 is a blocking capacitor to keep d.c. out of the current meter and
generator. As in the preceding example, values of L and C2 are chosen for zerosignal resonance below
the generator frequency. Because the capacitance of C1 is very high with respect to that of C2, it has
negligible effect on circuit tuning.
Nonlinear ParallelResonant Circuit
Fig. 5. Parallel resonance with a nonlinear circuit element.
It is well known that the current in the line supplying a parallelresonant circuit dips to a low
value when the circuit is tuned to resonance at the generator frequency. If a voltagetuned element
is included in the parallelresonant circuit, the circuit will then resonate at only one value of input
voltage. The line current will then decrease at this voltage level, showing a negative slope.
Fig. 5A shows a circuit for displaying this negativeresistance effect. The parallelresonant circuit
is composed of aircore coil (L) and a 56 pf. (μμf.) Varicap semiconductor voltagevariable capacitor
(C2). C1 is a blocking capacitor (0.005 to 0.01 μf.) whose capacitance is so high with respect to
C2 that only the latter determines the circuit tuning. The values of L and C2 are chosen such that the
zerosignalvoltage resonant frequency of the circuit is somewhat lower than the generator frequency.
As the generator voltage (E_{R.F.}) is increased, the current (I_{R.F.}) increases from
zero to point A in Fig. 5B. The increasing voltage reduces the capacitance of C2. At the particular
level of signal voltage, the corresponding C2 value tunes the circuit to resonance at the generator
frequency, and the line current dips to point B. As the voltage is increased further, the capacitance
decreases still more, tuning the circuit above resonance, and the current again rises to point C and
beyond. Along the negative slope, AB, the current is decreasing as voltage is increasing.
For best results, the generator frequency should not be lower than 20 mc. The higher the frequency,
the more pronounced is the negativeresistance effect.
Diodes at Higher Frequencies
At high radio frequencies, the combined action of nonlinear capacitance and a.c. rectification provided
by the semiconductor voltagevariable capacitor gives rise to an a.c. negativeresistance effect (as
well as to hysteresis, in some cases).
Heizman has described a microwave setup in which the capacitor diode is operated in a tunable waveguide.^{5}
The negative resistance and hysteresis obtained with this arrangement have been utilized for switching
at microwave frequencies. The response curve is similar to those of Figs. 1B and 3C.
The conventional pointcontact germanium diode has been known to exhibit negative resistance at very
high frequencies.
North observed that individually welded whisker diodes showed this effect when used as v.h.f. superhet
converters.^{6}
Such a.c. negative resistance has been observed in some conventional diode tubes operated at u.h.f.^{7,8}
This is a secondary effect resulting from electron transit time in the tubes. The mechanism involves
the dynamic plate resistance of the diode, which decreases at ultrahigh frequencies. When the transit
time equals the period (1/f) of the applied voltage, R_{p} = 0. At higher values of
transit time, R_{p} is first above then below zero, its oscillating curve showing a negative
slope in some portions.
Feedback Amplifiers
An amplifier provided with the proper amount of positive feedback may present negative resistance
to circuitry connected to its input terminals. This applies to amplifiers of all types, such as vacuumtube,
transistor, magnetic, dielectric, and varactor. It is this very property that is utilized so widely
in oscillating and regenerative circuits; the negative resistance provided by the feedback amplifier
cancels the losses of the tank circuit into which it operates. A familiar example, in which loss cancellation
results in a large increase in figure of merit, is the "Q"multiplier.
The groundedgrid amplifier operates very effectively as an a.c. negativeresistance device and has
been exploited in telephony as a twoway repeater.
A general limitation of all a.c. negativeresistance devices is their requirement of an a.c. supply,
which is sometimes inconvenient and which always limits the maximum speed at which the device operates.
When a.c. supply and circuitry are already provided, however, or the application is of an a.c. nature
to start with, and the supply frequency is high enough to permit maximum desired operating speed, a.c.
negativeresistance devices offer distinct advantages.
References
1. Turner, Rufus P.: "Negative Resistance: What It Is & How It's Used," Electronics World,
May 1961.
2. Isborn, Carl: "Ferroresonant FlipFlops" Electronics, April 1952
3. Rutishauser, R. W.: "Ferroresonant FlipFlop Design," Electronics, May 1954.
4. Triest, W. E.: U.S. Patent No. 2,709,757 (May 31, 1955).
5. Heizman, C. L.: "Microwave Bistable Circuits Using Varactor Diodes," Proceedings of the IRE, April,
1961.
6. Torrey. H. C. & Whitmer, C. A.: "Crystal Rectifiers," McGrawHill Book Co., New York, 1948,
pgs. 362, 391.
7. Llewellyn, F. B. & Bowen, A. E.: "The Production of Ultrahighfrequency Oscillations
by Means of Diodes," Bell System Technical Journal, April 1939.
8. McPetrie, J. S.: "A Diode for UltraHF Oscillations," Experimental Wireless and Wireless Engineer,
March 1934.
Posted February 7, 2017
