Page 192 - Op Amps Design, Applications, and Troubleshooting

Wien-Bridge Oscillator 175

amp portion of the circuit is determined by the ratio of the feedback resistor (R f)
and the effective resistance of the field-effect transistor (FET) in parallel with Rj.
The FET's resistance is determined by the amount of bias voltage on the gate. As
the voltage on the gate becomes more negative, the channel resistance in the FET
is increased.
The gate voltage for the FET is obtained from the output of a half-wave rec-
tifier and filter combination. The input to the rectifier is provided by the output of
the oscillator. In short, if the output amplitude tried to increase, the output of the
rectifier circuit would become more negative. This increased negative voltage
would bias the FET more toward cutoff (i.e., higher channel resistance). The
increased FET resistance would cause the gain of the op amp circuit to decrease
and thus prevent the output amplitude from increasing. A similar, but opposite,
effect would occur if the output amplitude tried to decrease.
The output signal is also returned to the (+) input terminal (positive feedback)
via the R^ and R 2C 2 network. This is the frequency selective portion of the oscilla-
tor. At the desired frequency of oscillation, the RC network will have a voltage gain
of one-third and a phase shift of zero (i.e., no phase shift). At all other frequencies,
the loss will be even greater and the input/output signals will differ in phase.
Now, if the amplifier portion of the circuit can provide a gain of 3 and the fre-
l
quency selective portion of the circuit has a gain (actually a loss) of /$, then the
overall closed-loop gain will be 1, or unity, at the frequency of oscillation. We
now have the conditions necessary for oscillation. Additionally, since the gain of
the amplifier is self-adjusting because of Qi, we also have the conditions necessary
for a stable output amplitude.

4.2~2 Numerical Analysis

Let us now analyze the Wien-bridge oscillator circuit shown in Figure 4.2 in
greater detail. The most important characteristic to be evaluated is the frequency
of operation. This is solely determined by the R^ and R 2C 2 networks. Although
oscillators can be made with unlike values of resistance and capacitance, using
equal values for the resistors and equal values for the capacitors in the R-tQ and
R 2C 2 networks is the general practice. This greatly simplifies the design and analy-
sis of the Wien-bridge oscillator. When equal sets of values are used for the bridge,
the frequency of oscillation is given by Equation (4.1).

In the case of the circuit in Figure 4.2, the frequency of operation is computed as

The voltages at the various points in the circuit are not readily computed
because they are highly dependent on the specific FET being used in the circuit.
We know from our basic oscillator theory that the amplifier must have a voltage