July 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.
It appears that
maybe Abraham Lincoln had a son who was an electrical engineer working at Motorola Semiconductor
back in the 1960's. Put glasses on Honest Abe (I did) and author Irwin Carroll's a spitting
image of the Great Emancipator. Seriously though, this article is a great introduction
to the fabrication and use of variable capacitance (aka varicap and varactor) diodes.
They have been - and still are - used widely for electrically tunable oscillator and
filter circuits. Topics such as temperature and figure of merit ("Q") are discussed as
This edition of Electronics World ran a series of diode articles:
Hot Carrier Diodes,
Diodes, Tunnel Diodes,
Microwave Power Diodes,
A Survey of Silicon
Junction Diodes, and
For the past three years the author has been responsible for disseminating
technical information about Motorola products and developments. In this capacity he has
worked with research engineers, production engineers, application groups, and product
marketing personnel. Prior to joining the company, he worked for Ameco, Inc., preparing
training material on use and maintenance of CATV equipment.
By Irwin Carroll / Supervisor
Technical Communications, Motorola Semiconductor Products Inc.
Diodes whose junction capacitance is variable with voltage are beginning to replace
large bulky tuning capacitors. Here are the operating principles and important parameters.
Varactor diodes, or variable-capacitance diodes, are semiconductor diodes that have
been optimized for the capacitance effect under reverse-bias conditions. Basically, they
can be divided into two main applications categories: tuning and harmonic generation.
As might be expected, they have different characteristic requirements, but do share the
common trait of having a junction capacitance that is variable with voltage.
Fig. 1 - Behavior of depletion region under various bias conditions.
The most commonly used symbols are shown.
Fig. 2- Equivalent circuits for a varactor diode.
The capacitance effect in a varactor arises from the depletion region separating the
p and n material in a diode. Recalling simple junction physics, the depletion region
has a high resistivity because of the lack of mobile carriers and, as such, makes a good
dielectric. When a reverse bias is applied to the diode, the depletion region is widened
and if slightly forward-biased (not enough to cause forward conduction), the depletion
region narrows. Fig. 1 is a simplified diagram of how bias affects the junction. The
p- and n-doped regions are the "conductive plates" and, of course, the closer the plates
of a capacitor, the higher the capacitance value, so that at zero, or slightly forward
bias, the maximum capacitance value is reached. The minimum capacitance occurs when the
depletion region is widest - at reverse breakdown voltage.
Used as a tuning diode, a varactor is biased between zero voltage and reverse breakdown
voltage. (Actually parametric amplifiers would also fall into this category but will
not be discussed in this article.) The equivalent circuit for a varactor diode is given
in Fig. 2A. For low-frequency operation, the circuit reduces to that of Fig. 2B.
Doping profiles of varactors vary according to their intended use. Fig. 3 shows the
four most common types encountered. The abrupt and hyper-abrupt junctions are used for
tuning while the linearly graded and step-recovery junctions are used for harmonic generation.
The abrupt junction can also be used for harmonic generation, but because the second
harmonic predominates, it is impractical for high harmonics.
The step-recovery diode is a departure from the normal varactor since the capacitance
change is quite small and occurs mostly near zero bias. Also, the step-recovery device
makes use of forward bias and charge storage. The phenomenon that occurs is not too different
from the reverse-recovery action of a common rectifier diode. Simply stated, when the
junction is slightly forward biased, charge carriers from one region are injected into
the other to form minority carriers in that area. If the lifetime of the carriers is
longer than the period of the applied forward voltage, when the reverse voltage is impressed
across the junction, most of the carriers are returned to their point of origin in a
compact bunch. While the carriers are returning, there is a high reverse current flowing;
when they reach their point of origin, the current flow ceases abruptly.
The steep current waveform generated is rich in harmonics and when added to the other
non-linearities of the varactor enhances its multiplier function. Step-recovery varactors
have been used to obtain useful output levels for frequencies as high as the 25th harmonic
of the input. Such devices are very economical when it is necessary to obtain crystal-controlled
frequencies in the microwave region. Other devices can produce as much as a watt of power
in the 12-GHz region (doubling from 6 GHz).
Fig. 3 - Doping profiles for various varactor diodes.
Fig. 4 - (A) Normalized curve of capacitance vs reverse voltage for
abrupt-junction diode. (B) Typical capacitance vs reverse voltage for the hyper-abrupt
Fig. 5 - (A) Varactor-tuned circuit with diode for temperature compensation.
(B) Using diodes back-to-back to reduce intermodulation distortion. (C) Varactors used
as variable coupler. (D) Double-tuned circuit using parallel resonance. (E) Same but
using series resonance.
As a variable capacitor, the varactor is rugged and small, is not affected by dust
or moisture, and is ideal for remote control and precision fine tuning. The current uses
of tuning diodes span the spectrum from AM radio to the microwave region. Presently the
cost of varactor tuning is a little higher than conventional methods but the cost is
coming down quite rapidly as sales volume increases.
The most significant parameters of a tuning diode are the capacitance ratio, "Q",
series resistance, nominal capacitance, leakage current, and breakdown voltage. For high-frequency
operation, the package parasitics are also important considerations.
The capacitance ratio, which defines the tuning range, is the amount of capacitance
variation over the bias voltage range. It is normally expressed as the ratio of the low-voltage
capacitance divided by the high-voltage capacitance. For example, a typical spec which
reads C4/C60 = 3 indicates that the capacitance value at 4 volts
is 3 times the capacitance value at 60 volts. The high voltage in the ratio is usually
the minimum breakdown voltage specification. A 4-volt lower limit is quite common since
it describes the approximate lower limit of linear operation for most abrupt-junction
The curve in Fig. 4A is a normalized bias vs capacitance relationship for abrupt junctions
and if the capacitance at a given reverse bias is known, the capacitance at other voltages
can be determined. This curve follows the relationship:
where: CT = total capacitance, Cc = case capacitance (about
0.17 pF for glass diodes), C0 = junction capacitance at zero bias, VR
= reverse bias voltage, φ = contact potential (about 0.6 V for silicon) , and γ
= power law of the junction (determined by doping gradient and is approximately 0.45
for abrupt junctions).
The capacitance ratio of tuning diodes varies in accordance with construction. Diffused
tuning diodes are usually limited to a 4:1 capacitance ratio; alloy types, 5:1; and hyper-abrupt
junctions can have ratios of 20:1 and higher.
The hyper-abrupt diode, because of its doping gradient (see Fig. 3D) , has a γ ≈
2. A typical bias vs capacitance curve for this type of diode is shown in Fig. 4B. Particular
effort has been devoted to this type of diode because of its high capacitance ratio potential.
Indeed, it is the only type suitable for tuning the AM broadcast band, which requires
a minimum tuning ratio of 10:1.
Temperature Stability & Figure of Merit
The temperature stability of a tuning diode is related to contact potential, φ
As shown in Eq. (1), temperature effects will be greatest at low values of reverse bias
and will become minimal for high values of VR Changes in φ of 1.5 to 2.7
mV/°C are typical. This variation can be compensated, if necessary, by using a silicon
diode with the same temperature coefficient in the bias supply, as shown in Fig. 5A.
The figure of merit or "Q" of a tuning diode should be specified at a given reverse
bias and frequency. However, rather than stating "Q", series resistance at a given bias
might be more practical. As shown previously in Fig. 2, RS is in series with
CJ but RS is also variable with bias, decreasing in value as bias
voltage increases. The "Q" for a capacitor with a series resistance is given by:
Q = 1 / (2πfCRS) ..........(2)
where: f = frequency in Hz, C = capacitance in farads, and RS
= series resistance in ohms.
As reverse bias increases, both C and RS decrease, so that at a given frequency,
"Q" is greatest n t the highest reverse bias. For example, a diode that has a "Q" of
500 at 50 MHz and 2 voltss reverse bias could have a "Q" of 2000 at the same frequency
and 20 volts reverse bias. With this relationship in mind, if a tuned circuit is designed
so that the highest frequency corresponds with a bias voltage that is at or near the
maximum operating point, "Q" will be greatest at the highest frequency. Since selectivity
is a function of "Q", selectivity will also he highest at the high end of the operating
Ideally, tuning diodes should have high "Q", low series resistance, low reverse leakage,
and high breakdown voltage at any desired capacitance ratio; however, as might be expected,
these parameters are not unrelated and improving one degrades another so that often a
compromise must be reached. As a rule, diodes with low capacitance values have the highest
"Q" and where this is the most important parameter, as in the high-selectivity tuners,
the smallest possible capacitance value diode should be used. If large variations in
operating temperature are expected, and temperature stability is the greatest need, large
capacitance values should be chosen so that bias voltage can be kept at a high level.
Fig. 6 - AM radio front-end using varactor-diode tuning.
One of the simplest forms of varactor-tuned circuit was shown in Fig. 5A (with the
compensating diode and R1 removed). Capacitor C1 is used for d.c. blocking and R2 (several
hundred kilohms) provides isolation. However, in some applications the a.c. swing in
the circuit might cause intermodulation distortion. Two things can be done to minimize
this effect: (1) the a.c. signal should be as small as possible, and (2) a back-to-back
pair of tuning diodes can be employed.
In the first case, for a given power level, low-impedance circuits have lower voltage
swings - and voltage is the tuning mechanism; however, to maintain high "Q", the L/C
ratio should be as small as possible. Fig. 5B is an example of the back-to-back diode
method of reducing intermodulation. Note that the d.c. blocking capacitor is no longer
necessary. This particular configuration is also useful as a variable coupling capacitor,
as shown in Fig. 5C.
When operating at very high frequencies, the diode inductance, which has been ignored
thus far, must be taken into account. As an example, the double-tuned, parallel-resonant
circuit shown in Fig. 5D is useful at relatively low frequencies but has serious limitations
at frequencies high enough for the diode inductance to become effective. Fig. 5E shows
a double-tuned, series-resonant circuit where the diode inductances simply add to the
circuit inductances and so do not degrade performance. By using series-resonant techniques,
varactors have been successfully applied to the tuning of microwave cavities.
The development of hyper-abrupt junction diodes, with their high tuning ratios suitable
for AM radio tuning, has stimulated a new and higher interest in such devices. This is
particularly true because of the many advantages they present for car radios which can
be unhitched from their normal dash-mounted positions and placed in more easily accessible
Fig. 6 shows the front-end of an AM radio modified for electronic tuning by means
of varactor diodes. In this application, or any other where two or more stages are tuned
simultaneously, matching of the diodes is important if the stages are to track one another.
This means that the voltage vs capacitance curve for the diodes must be nearly the same.
For the circuit in Fig. 6, a tracking error of up to 2 percent provided good results.
By adding a ramp-voltage circuit and search oscillator to the circuit, search-tuning
becomes a compact possibility. The frequency can be monitored by a voltmeter (measuring
the bias voltage) calibrated in terms of frequency. Precision tuning can be achieved
by using a multi-turn potentiometer in the bias supply.
Another obvious application for tuning diodes is for frequency modulation. The circuit
of Fig. 7 has a center frequency of 52 MHz with a frequency deviation of ±75 kHz.
Voltage input, ΔV, is limited to ±200 mV with the polarity chosen
so that a positive ΔV corresponds to an increase in the diode reverse-bias voltage.
Other Circuit Applications
Fig. 7 - A frequency modulator using a varactor diode.
Step-recovery varactors are commonly used for high-order harmonic generation. Typical
efficiencies may run around 30 percent for an 8X multiplication down to around 10 percent
for a 25X multiplication.
The step-recovery diode can be used to great advantage as a duplexer, permitting a
single antenna to be used for both transmitting and receiving. Normally, p-i-n varactors
are used for this application but have the disadvantage of requiring an external bias
In multiplier applications, the power dissipation of the varactor becomes an important
consideration. Also, the efficiency, η, defined as Pout/Pin
is important. The latter is highly dependent on the multiplying factor, being as high
as 75 percent for doubling and dropping to 10 percent for X25.
Although the cost of varactor tuning is slightly higher than mechanical methods, the
advantages gained are usually well worth the difference. Compact, reliable, and what
would be otherwise impractical circuits have been developed with tuning diodes. Gallium-arsenide
tuning diodes for parametric amplification cost as much as $400, silicon devices for
u.h.f. and microwave tuning, $12; matched sets of hyper-abrupt junction diodes for AM
tuning, less than $3 each, and plastic encapsulated diodes for tuning and a.f.c. applications
in the v.h.f. TV and FM areas, less than $0.40 each. (These are all small-quantity prices;
however, as usage, hence volume, increases the price will drop to very competitive levels.)
Varactors for harmonic generation can cost from $20 to $150 with several high-quality
units (up to 12-GHz operation) costing less than $60. New devices such as Gunn-effect
and IMPATT diodes and higher frequency transistors are reducing the need for some types
of varactors but usage continues to grow. Two important areas of this growth are duplexing
and digital phase shifting.
Posted February 21, 2018