November 15, 1965 Electronics
[Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from Electronics,
published 1930 - 1988. All copyrights hereby acknowledged.
I remember in one of my circuits
classes in college when the gyrator was introduced, and I thought it was an ingenious invention.
The gyrator circuit, implemented with an operational amplifier (opamp) and a couple resistors
and capacitors, changed its measured impedance type from that of a capacitance to that
of an inductance. That is, its impedance represents an R + jX Ω
format. Frequency limits are imposed by a combination of the self-resonant frequencies
of the resistors and capacitors as well as the
product (GBWP) of the opamp, and power handling is primarily limited by the opamp's
voltage and current capabilities. You might ask why, with all those constraints on its
use you would even want to use a gyrator circuit? The answer is that within its limitations,
the gyrator often represents a less expensive and more compact version of a physical inductor.
This is particularly true with integrated circuits (ICs) where, unless it is a
monolithic microwave IC (MMIC) operating in the tens of gigahertz
region, there is no space available on the die for a printed metallic inductor with enough
inductance to be useful. Any inductors would need to be mounted off-chip on the PCB with
I/O pins interfacing to the IC. Gyrators onboard ICs have made filtering functions available
into the tens of megahertz realm nowadays with the extremely high GBWP of modern opamps.
Six Possible Routes to Noninductive Tuned Circuitry
Inductance is nearly impossible to put into an IC,
but the effect can be achieved using RC networks, digital filtering, acoustic resonators
or semiconductor delay lines.
By Vasil Uzunoglu, Applied Physics Laboratory
Johns Hopkins University, Silver Spring, Maryland
When circuit designers began shifting from tubes to transistors, they also began to
seek ways to do away with bulky transformers and coils. One approach was to use resistance-capacitance
(RC) networks as substitutes for low-frequency inductance-capacitance (LC) circuits.
With the arrival of integrated circuits, the designers no longer have a choice. No
practical method has been found for putting usable amounts of inductance into an integrated
circuit, despite some qualified successes. Multilayer thin films, deposited on monolithic
chips, can provide a few microhenries of inductance; however, such small inductances
are not adequate for operation at frequencies lower than a few megacycles per second.
More recently, an electromechanically resonant field-effect transistor has been introduced
[Electronics, Sept. 20, 1965, p. 84], but its ultimate utility is yet to be proved.
Two typical notch-filter RC circuits are the parallel-T at left and
the bridged-T, center. The attenuation vs. frequency relationships for minimum and nonminimum
phase-shift networks are similar, as shown at right.
The engineer who wants to design a frequency-sensitive integrated circuit must find
some way to duplicate the effect of inductance. There is no single perfect substitute
for inductance, but at least six techniques are known; the choice depends on the requirements
of the system being designed.
Three of these techniques employ resistor-capacitor networks. One uses RC notch filters
in the feedback path; another, RC circuits in the forward transmission path; and the
third, negative impedance converters. These methods have the same disadvantage: in some
applications, particularly those in which high Q values (100 or larger) are needed, RC
networks have a tendency toward instability. In such cases, three other techniques are
possible: sampling (digital filtering), using acoustic resonators, and using semiconductor
The choice of one of these six approaches depends on the specific requirement; it
should be based on a careful evaluation of the specifications, and on the comparison
of these requirements with the inherent advantages and disadvantages of each method.
A notch-filter circuit is one whose gain-versus-frequency characteristic exhibits
a steep drop or rise at resonance. A typical voltage-gain curve for a notch-filter circuit
is shown on page 115. Also shown are two examples of notch-filter circuits: the parallel-T
network and the bridged-T network.
Notch-filter circuits fall into two general categories: one called a minimum phase-shift
type, the other called a nonminimum type. The minimum type exhibits a phase shift less
than ±90°. The latter can produce shifts in phase from 0 to 360°. This
is shown by the curves on page 115. Minimum-phase-shift circuits are usually fabricated
with lumped elements, nonminimum types are made with either lumped or distributed elements.
Phase characteristics for minimum and nonminimum phase-shift notch
filters differ greatly, although attenuation characteristics are similar. The nonminimum
circuit produces phase shifts from 0° to 360°; the minimum filter circuit exhibits
shifts smaller than ±90°.
Simplified representation of an amplifier with a notch filter in the
feedback path. The filter may be of either the minimum or nonminimum phase-shift type.
When high Q is desired, the nonminimum type is preferable, but such circuits can be
unstable. For a high degree of stability, when lower Q can be tolerated, the minimum
type is usually best. For stable oscillator circuitry,2 however, the nonminimum
circuit is preferred because of the sharper phase shift with changes in frequency.
Either type of network can be constructed using a bridged-T arrangement. If a minimum
phase-shift circuit is desired, lumped resistors are used for R1 and R2.
For nonminimum phase shift, R1 and R2 should be distributed elements.
Both minimum and nonminimum phase-shift networks can be realized with lumped elements
using the parallel-T circuit but the nonminimum network requires more reactive (capacitive)
A nonminimum phase-shift circuit must have at least three capacitors.1
However, the circuit can be designed so that the distributed resistors also contribute
the required capacitance values.
A simple block diagram for an amplifier that incorporates a notch filter in the feedback
path is shown on this page. Regardless of whether it is a minimum or nonminimum circuit,
a notch filter must satisfy two circuit requirements: the required Q must be obtained,
and the insensitivity to minor variations in operating conditions must be sufficient
to prevent oscillations.
The closed-loop transfer function (gain including feedback) is given by:
where AT is the total closed-loop gain, eout
is the closed-loop output voltage, ein is the input
voltage, A(s) is the open-loop gain of the amplifier (gain
without feedback), β(s) is the feedback factor,
β(s) = Δeout/eout, where
Δeout is the feedback voltage.
To achieve the required Q without oscillations, the amplifier design must satisfy
the conditions that |A(s)β(s)| ≈ 1 and the phase
shift over the loop is approximately 360°. If the |Aβ| is actually unity, and the
phase shift 360°, oscillation would occur. Therefore, this product and phase angle
should be approached but not actually reached.
The sensitivity of the gain for a closed-loop system1 may be defined as:
where dAT is the variation caused by
etc., where T is the period of the modulating function. The multiplied signal is then
fed to a low-pass filter, h(t). The frequency difference between
f(t) and ein must lie
within the bandpass limits of h(t). The outputs from the filters
are multiplied again by functions Φ(t), Φ(t - T/N, Φ(t
- 2T/N), in synchronism with f(t).The outputs from all
branches are added up; this sum constitutes the final output. The entire operation simulates
the functioning of a series-tuned LC network that passes a desired frequency and rejects
all other frequencies.
Pole plot for bandpass filter.
Because the modulating signals are sinusoidal, the driving-point (input) impedance
of the entire network can be represented by.
where ωo is 2π
times the center frequency and K is a constant determined by
the circuit elements. Equation 7 is also the expression for the impedance of an inductor
in series with a capacitor.
If the modulating time function, f(t) is an impulse and
if the input signal is supplied by a current source each modulator can be replaced by
a simple switch. Then the input and output modulating signals are equivalent to a pair
of rotary switches with N contacts as a common shaft that rotates at
1/T = ωo/2 cycles per second. Each low-pass filter,
h(t), must have a bandwidth much lower than
fo, the center frequency desired for the entire
When only one passband is desired, the bandpass-filter circuit must have at least
three h(t) sections to get rid of the harmonics (multiples
of ωo). A mechanical sampling section for eliminating
harmonics8 is depicted at the left. Each filter samples at a different time.
As the switch's operating speed increases, the effectiveness of stopping the harmonics
The extent of time during which the brushes remain on each contract is given by:
t1 = T/R1 and t2
= T/R2 (8)
where t1, t2
are contact times, R1 is the source impedance, and
R2 is the load impedance.
An advantage of this technique is that the filter can be tuned at different frequencies
without altering the system. The center frequency of the filter can be changed simply
by changing the frequency of the timing source that controls the switching rate. With
this method, it is possible to achieve Q's of 5,000 to 10,000 at a few hundred kilocycles
per second. These values are much higher than those that can be obtained with any type
of stable filter using RC networks.
Mechanical switching circuit for frequency filtering. Each filter
represented by h(t) samples at a different time. The rejection of harmonics is improved
by increasing the switching speed.
Electrical equivalent of the comb data-sampling circuit.
Besides its use as a very narrow bandpass filter, the same system can be used to build
comb filters,8 with bandpass centered at multiples of ωo.
In the simplified mechanical analog of a comb system, shown on page 119,
t1 is the time required by the brush to move from
one contact to another. The input signal is applied through a high-value resistor to
brush A (upper arrow on diagram). While A is in contact with the corresponding capacitor,
the capacitor begins to charge, so that its potential approaches that of the input signal.
However, the time constant of the RC network is much higher than the dwell time of the
brush on one segment, so that it takes a certain time for the capacitor to charge; before
the capacitor can build up an appreciable charge, the brush changes position.
If the signal frequency is a multiple of the frequency of rotation, the signal will
have the same value each time the brush comes in contact with a given segment. Thus,
after a certain number of revolutions, the potential across each capacitor will attain
its maximum value; this means that the locus of charge on the capacitors is an indication
of the input-signal level. However, this system prevents the buildup of random signals
and signals that are periodic, or of signals that are periodic but whose frequency is
not a multiplier of the rotational frequency. This suggests that such a sampling filter
may be used in detecting weak periodic signals in the presence of noise.
An electrical circuit equivalent of the mechanical data-sampling filter just discussed
is shown on this page. This circuit was introduced by G. H. Danielson."
The acoustic-resonator technique requires mounting piezoelectric crystal onto a monolithic
silicon chip. The installation is difficult, because the crystal must be positioned so
that it is allowed to vibrate freely.
When an electric wave is applied to the resonator, traveling acoustic waves are generated
at the resonant frequency.2 These traveling waves are reflected when they
reach a boundary. If the resonator is well designed, the initial transmitted and reflected
acoustic energy are added together, causing an intense standing wave. This acoustic wave
is converted back to an electric wave at the point of application. At this point the
electrical circuit sees the equivalent of a parallel circuit tuned to the resonant frequency.
To achieve high Q, the losses must be minimized. The acoustic wave, as it bounces back
and forth, is subject to high losses. The use of an acoustic resonator in microelectronic
blocks is feasible if the supporting medium of either the resonator or substrate does
not absorb the mechanical vibrations or permit leakage of the acoustic energy. Therefore,
solid mounting of a conventional piezoelectric resonator is not possible. Piezoelectric
materials such as cadmium sulfide and zinc oxide have been used for acoustic resonators.
Semiconductor Delay Lines
Semiconductors delay lines1 are relatively easy to integrate because only
one diffusion is required in their manufacture. Only resistive elements used; capacitors
are eliminated. In the semiconductor delay line shown on this page, the distance between
the two n regions determines the delay time and, therefore, the frequency.
Minority carriers are injected at the junction on the left and, being subject to an
electric field, are diffused and drift to the right. When minority carriers are subjected
to an electric field, they cause a phase shift Φ which
is given by:
where t0 is the time delay, ω1
is the lower bandpass limit frequency, and ω2
is the upper bandpass limit frequency. The delay is a function of the length of the semiconductor
path, as noted above, also of the intensity of the electric field. If a delay line is
inserted in the feedback path of an amplifier, it will cause a phase shift and attenuation,
which will determine the closed-loop gain and phase.
Mechanical analog of a comb filter. Here the mechanical rotational
frequency of the switch fixes the location of the passbands, and the time constant (R2
times the capacitor being touched by the brush) fixes the width of each band.
Semiconductor delay line. The time delay is a function of the distance
between n-type silicon regions. The stability criterion of a circuit using a semiconductor
delay line is similar to that of a network using an RC feedback circuit such as a notch
The same stability relations discussed earlier in this article for an RC network placed
in an amplifier's feedback circuit also apply if a delay line is substituted for the
In general, an RC notch filter in the feedback path provides poor stability unless
the Q requirements are not formidable. RC networks in the forward transmission path provide
good stability but poor Q values. With a negative impedance converter, both the stability
and Q obtainable are somewhat better. All three methods have the disadvantage that they
cannot provide high stability and a high Q simultaneously. Digital filtering can, but
it has the disadvantages of complexity and associated high cost.
Acoustic resonators are a recent development. One big disadvantage of these is that
fabrication of circuits containing such devices is difficult. Semiconductor delay lines
can be made small and are relatively easy to integrate.
1. Vasil Uzunoglu, "Semiconductor Network Analysis and Design," Chapters 10 and 16,
McGraw-Hill Book Co., 1964.
2. W.E. Newell, "Tuned Integrated Circuits," Proceedings of the IEEE, December 1964,
3. J.G. Linvill, "Transistor Negative-lmpedance Converters," Proceedings of the IRE,
June 1953, Volume 41, pp. 725-729.
4. A.I. Larky, "Negative Impedance Converters," IRE Transactions on Circuit Theory
CT-4, September 1957, pp. 124-131.
5. W.R. Lundry, "Negative Impedance Circuits-Some Basic Limitations," IRE Transactions
on Circuit Theory CT·4, September 1957, pp. 132·139.
6. T. Yanagisava, "RC Active Networks Using Current Inversion Type Negative Impedance
Converters," IRE Transactions on Circuit Theory CT-4, September 1957, pp. 140-144.
7. L.E. Franks and I.W. Sandberg, "An Alternative Approach to the Realization of Network
Transfer Functions," The Bell System Technical Journal, September 1960, pp. 1321-1350.
8. W.R. DePage, et al., "Analysis of a Comb Filter Using Synchronously Commutated
Capacitors," Electrical Engineering, March 1953, pp. 63-68.
9. G.H. Danielson, et al., "Solid State Microelectronic Systems," General Electric
Report No., AD 426938, 1963.
Vasil Uzunoglu's book, "Semiconductor Network Analysis and Design," was published
last year by the McGraw-Hill Book Co. He holds six patents and has applied for six more.
On Nov. 1 he joined the Arinc Research Corp. in Annapolis, Md., as a scientist in the
devices research program.
Posted November 13, 2018