January 1962 Popular Electronics
[Table of Contents]
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Bypass capacitors play a vitally important role in electronic
circuit design. Many people do not know the proper way for deciding
which capacitor or capacitors is/are needed for effective noise
and/or signal bypassing without either overdoing or underdoing
it. Needs change over the years as frequencies and signal characteristics
occupy new realms of the spectrum. A Fourier analysis of some
of today's complicated waveshapes for switching power supplies
shows how sometimes tailored responses to bypassing is required.
This article from the January 1962 Popular Electronics does
not delve into the intricacies of complex filters, but it does
provide a nice introduction to the need for bypassing and how
to stand a good chance of being successful at it. In rare instances,
no amount of bypassing will solve problems with spurious signals
and a more engineered approach is required where the functional
circuit needs to be modified (I know this from experience!).
Here is an article written by RF Cafe contributor
Carl Lodstrom on the subject of bypassing.
Getting to know the... Bypass Capacitor
By John M. Doyle
National Radio Institute
Capacitors are used in modern electronic circuitry for such
purposes as blocking, filtering, timing, and bypassing. The
last-mentioned application - bypassing - is by far the most
common. It's also much more critical than many people suspect,
since the selection of a wrong-value bypass capacitor can result
in poor frequency response, phase distortion, circuit instability,
or even outright oscillation.
Now, you may feel that this problem is no concern of yours,
but is rather one for the design engineer. "Shucks," you say.
"If a capacitor-bypass or otherwise - goes bad, I'll replace
This approach works fine in most cases. But how many times
have you wished you could help fix a piece of equipment after
a well-intentioned, but poorly instructed, do-it-yourself fan
has been hard at work with his trusty soldering gun? Or how
many times have you felt like throwing that cheap "screech-box"
receiver out of the window, when a 15¢ bypass capacitor would
do much to quiet the demon of temptation? Finally, remember
that despite our ultra-modern manufacturing methods, "goofs"
are still made by people who do the physical wiring and inspection
but who know nothing about the workings of the circuit.
If you're now convinced of the importance of knowing a little
more about bypassing (and shame on you if you aren't), let's
get on with the job.
Reactance. When a capacitor is used as a
bypass, it must provide a low-impedance path for electrical
currents of certain frequencies and a high-impedance path for
those of other frequencies. The property which permits it to
operate in this manner is called reactance. The value of reactance
for a given frequency is determined by the basic formula:
Xc = 1 / (2π f C)
where Xc is the capacitive reactance in ohms,
2π is a constant (approximately 6.28), f is the operating
frequency in cycles per second, and C is the capacitance in
This relationship tells us that the reactance of a given
capacitor decreases as frequency increases. For example, the
value of Xc for a 0.01-μf. capacitor at a frequency
of 500 cycles is about 31,800 ohms. But at a frequency of 5000
cycles, the reactance has decreased to about 3180 ohms.
Not only must we be able to calculate Xc, but
we must also know how to determine what value capacitor is needed
to obtain a certain reactance at some specified frequency. All
that we have to do is rearrange the above equation as:
= 1 / (2π f Xc)
where all symbols have the same meaning as before. For example,
if we want to know what value capacitor will provide a reactance
of 18 ohms or less at a frequency of 500 cycles, we just substitute
known values in the above formula. The calculated answer is
17.7 μf., approximately, but the next highest standard capacitance
value available will be okay for most applications.
Audio-Frequency Amplifiers. In a typical
audio-frequency amplifier, such as that shown in Fig. 1, a capacitor,
C1, is used to bypass audio frequencies around the cathode resistor,
R1. If capacitor C1 is omitted or if it does not operate properly,
the a.c. plate current component develops a voltage drop across
R1 which opposes the input signal applied to the grid. This
effectively reduces stage gain and results in inverse feedback
Fig. 1. Cathode bypass for audio amplifier
Now, let's see what requirements are placed on the capacitor
if it is to prevent degeneration. Suppose the amplifier is to
pass all frequencies between 100 and 5000 cycles, and the value
of cathode resistor recommended by the manufacturer for class
A operation is 1500 ohms. Because the reactance of the capacitor
decreases as frequency increases, a capacitor that satisfactorily
bypasses the resistor at the lowest frequency will work quite
nicely over the entire range.
A rule-of-thumb used by circuit designers is that the reactance
of the capacitor at the lowest frequency to be passed should
not exceed one-tenth the value of the resistor it bypasses.
Using this rule, we substitute known values in the equation
developed for finding C:
C=1/(6.28 x 100 x 150) = 11 μf
An electrolytic capacitor is suitable for this purpose because
its leakage resistance is not important and high capacitance
is obtained in a compact size.
In some applications, such as high-quality audio amplifiers,
the ratio of resistance to reactance at the lowest frequency
passed is made 20 to 1 or even higher, but the ratio used in
our example is adequate for most cases. Needless to say, the
working voltage of the capacitor selected for any bypassing
applications must be larger than the maximum voltage present.
Bypassing in the case of a transistorized audio-frequency
amplifier is very similar. A typical pnp transistor amplifier,
using the common-emitter arrangement, is shown in Fig. 2. Base
bias is obtained from the voltage-divider network, consisting
of R1 and R2, and the emitter is forward-biased (negative in
the case of a pnp transistor, and positive for the npn type).
To prevent signal degeneration, the emitter-bias resistor (R3)
is bypassed with a high-value electrolytic capacitor (C1).
Fig. 2. Emitter bypass for transistorized
In either type amplifier discussed above, a certain amount
of degeneration is sometimes intentionally used. Therefore,
before jumping to any wrong conclusion, always make sure that
degeneration is in fact undesirable before attempting to correct
a case of "faulty" design. If bypassing is improved where degeneration
is needed, the circuit will not operate properly.
Other Applications. When a pentode-type tube
is used, additional bypassing is needed in the screen grid which
must operate at ground potential, as far as all signal voltages
are concerned, if degeneration is to be avoided. A typical case
is the television i.f. amplifier shown in Fig.3.
Fig. 3. Screen bypass for typical i.f. amplifier
in a television set.
In this circuit, screen potential is obtained from the plate-supply
source through the screen-dropping resistor, R2. If bypass capacitor
C1 fails to operate properly at any frequency, the gain of the
amplifier falls off at that frequency. The value of C1 is again
determined by the rule-of-thumb that its capacitive reactance
at the lowest frequency passed should not exceed one tenth the
value of the resistor it bypasses.
mica or ceramic capacitors, ranging in value from about 50 μμf.
to 0.01 μf., are used for r.f. bypassing arrangements of this
type. If the pentode is employed as an audio-frequency amplifier,
high-quality paper or electrolytic capacitors are used. Their
proper value can be determined in the same way.
Sometimes it is necessary to bypass radio but not audio frequencies.
A typical case is in the detector circuit of an AM receiver,
as shown in Fig. 4. Assuming that the r.f. carrier frequency
is 455 kc., if the reactance of C1 is to be one-tenth the value
of R1 at this frequency, its value - using the formula previously
given - is approximately 75 μμf. We would use a standard 100-μμf.
mica or ceramic capacitor. If the highest audio frequency to
be passed is 5000 cycles, the reactance of the capacitor at
this frequency is better than 300,000 ohms.
Fig. 4. R.f. bypass for diode detector stage.
Another circuit in which bypassing is important is illustrated
in Fig. 5, where three amplifier stages are fed from a common
plate-voltage supply. Since most power supplies possess a finite
impedance, the output of V3 will be returned to the plate circuit
of V1 through load resistors R2 and R1. This effective signal
voltage is then fed to the grid circuit of V2 and then into
V3. Naturally, if the gain of these stages is high enough, oscillation
Fig. 5. Decoupling is required because of
feedback through R1 and R2.
To prevent instability of this type, decoupling networks
are used, a typical example of which is shown in Fig. 6. The
reactance of C1 and C2 at the lowest operating frequency is
made very small compared to the resistance of R3 and R4. Because
R3/C1 and R4/C2 form voltage dividers, almost the entire voltage
developed across the common impedance is dropped by R3 and R4.
Essentially, no feedback voltage is then coupled into the plate
circuit of V1 or V2.
Fig. 6. Networks R4/C2 and R3/C1 prevent
undesired feedback between stages.
The values of R3 and R4 should be kept as low as possible
to accomplish the job without dropping a prohibitive amount
of the d.c. plate voltage for V1 and V2. In cases where a very
small drop in this voltage is all that can be tolerated, R3
and R4 can be replaced by an inductance of low d.c. resistance.
The value of inductance needed for a given reactance at a specified
frequency is determined by the formula:
L = XL / 2π f
is the inductive reactance in ohms, and f is the operating frequency
in cycles per second.
Here's a final word about connecting bypass capacitors. At frequencies
of 30 mc. and below, the dimensions of the chassis are usually
only a fraction of a wavelength, and it can be considered a
fixed reference. Above 30 mc., however, the chassis is essentially
a conducting sheet on which points of maximum current and voltage
In the circuit of Fig. 7, grid and plate "ground" currents
pass through the chassis to the cathode of the stage. A good
practice, generally, is to separate these ground currents from
the chassis by returning all leads to the cathode or a bus bar.
Just be sure, however, that the leads are kept as short as possible
to prevent cross-coupling and undesirable feedback.
Fig. 7. Decoupling capacitors should be grounded
at one point for best results at high frequencies.
Posted September 17, 2012