Question 10.1: Determine the frequency for the Wien-bridge oscillator in Fi...
Determine the frequency for the Wien-bridge oscillator in Figure 10–12 . Also, calculate the setting for R_f assuming the internal drain-source resistance, r_{d s}^{\prime} , of the JFET is 500 Ω when oscillations are stable.
For the lead-lag network, R_1=R_2=R=10 \mathrm{k} \Omega and C_1=C_2=C=0.01 \mu \mathrm{F}. The frequency is
f_r=\frac{1}{2 \pi R C}=\frac{1}{2 \pi(10 \mathrm{k} \Omega)(0.01 \mu \mathrm{F})}=1.59 \mathrm{kHz}
The closed-loop gain must be 3.0 for oscillations to be sustained. For an inverting amplifier, the gain is that of a noninverting amplifier.
A_v=\frac{R_f}{R_i}+1
R_i is composed of R_3 (the source resistor) and r_{d s}^{\prime} . Substituting,
A_v=\frac{R_f}{R_3+r_{d s}^{\prime}}+1
Rearranging and solving for R_f ,
R_f=\left(A_v-1\right)\left(R_3+r_{d s}^{\prime}\right)=(3-1)(1.0 \mathrm{k} \Omega+500 \Omega)=3.0 \mathrm{k} \Omega
P R A C T I C E EXERCISE*
What happens to the oscillations if the setting of R_f is too high? What happens if the setting is too low?