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Wave Shaping

# Series RC Circuits

Series RC circuits are widely used for coupling signals from one stage to
another. If the time constant of the coupling circuit is comparatively long,
the shape of the output waveform will be almost identical to that of the input.
However, the output DC reference level may be different from that of the
input. The figure below, view A, shows a typical RC coupling circuit in which
the output reference level has been changed to 0 volts. In this circuit,
the values of *R* and *C* are chosen so that
the capacitor will charge (during *t*_{0} to *t*_{1})
to 20 percent of the applied voltage, as shown in view B. With this in mind,
let's consider the operation of the circuit.

At *t*_{0} the input voltage is -50 volts and the capacitor begins
charging. At the first instant the voltage across *C* is 0 and the voltage
across *R* is -50 volts. As *C* charges, its voltage increases. The
voltage across *R*, which is the output voltage, begins to drop as the
voltage across *C* increases. At *t*_{1} the capacitor has
charged to 20 percent of the -50 volts input, or -10 volts. Because the input
voltage is now 0 volts, the capacitor must discharge. It discharges through the
low impedance of the signal source and through *R*, developing +10 volts
across *R* at the first instant. *C* discharges 20 percent of the
original 10-volt charge from *t*_{1} to *t*_{2}.
Thus, *C* discharges to +8 volts and the output voltage also drops to
8 volts.

At *t*_{2} the input signal becomes -50 volts again. This -50 volts
is in series opposition to the 8-volt charge on the capacitor. Thus, the voltage
across *R* totals -42 volts (-50 plus +8 volts). Notice that this
value of voltage (-42 volts) is smaller in amplitude than the amplitude of the
output voltage which occurred at *t*_{0} (-50 volts). Capacitor *C*
now charges from +8 to +16 volts. If we were to continue to follow the operation
of the circuit, we would find that the output wave shape would become exactly
distributed around the 0-volt reference point. At that time the circuit operation
would have reached a stable operating point. Note that the output wave shape has
the same amplitude and approximately the same shape as the input wave shape,
but now "rides" equally above and below 0 volts. Clampers use this
RC time so that the input and output waveforms will be almost identical, as
shown from *t*_{11} to *t*_{12}.