(source: Electronics World, Aug. 1963)
By RUFUS P. TURNER
Description of ferroresonators, nonlineartype capacitors,
semiconductor capacitors, and other similar components.
The author's earlier article on negative resistance was devoted to directcurrent
devices." 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.
Fig. 1. Basic curves of the a.c. negativeresistance devices discussed
below.
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. lA, 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.
Fig. 2. (A) Basic ferroresonant circuit arrangement. (B) Test circuit showing
operation of the ferroresonant element. (C) Graph of operational characteristic.
Ferroresonator
The ferroresonator ( also called "ferroresonant circuit," saturablereactor
switch," and "ferristor ") is a special type of series resonant
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., determined by the inductance
and capacitance values. (Resonant frequency f, =1 / (6.28V LC) . 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, 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 (ELF) 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, 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
(OA 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. 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 risesin 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. 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.
Fig. 3. (A) Bask circuit arrangement using a nonlinear capacitor. (B)
Test circuit showing operation of the nonlinear element. (C) Response
of the test circuit.
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.
Fig 4. Alternative circuit with a semiconductor capacitor
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
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 negative resistance effect.
The parallel resonant circuit is composed of aircore coil ( L ) and
a 56 pf. (A pf.) Varicap semiconductor voltagevariable capacitor (C2).
C1 is a blocking capacitor (.005 to .01 uf) 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 (ER.F_) is increased, the current (IR.P.) 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.
Fig. 5. Parallel resonance with nonlinear circuit element.
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.
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, RnO. At higher values of transit
time, R, 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. Ishorn, 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.
