Question 15.5: Objective: Design a Wien-bridge circuit to oscillate at a sp...

The oscillation frequency given by Equation (15.52(b)) yields

ω_{o} = \frac{1}{RC}          (15.52(b))
RC = \frac{1}{2π f_{o}} = \frac{1}{2π(20  ×  10^{3})} = 7.96 × 10^{−6}
A 10 kΩ resistor and 796 pF capacitor satisfy this requirement. Since the amplifier resistor ratio must be R_{2}/R_{1} = 2, we could, for example, have R_{2} = 20  k\Omega and R_{1} = 10  k\Omega, which would satisfy the requirement.
Trade-offs: Standard-valued resistors R_{1} = 10  k\Omega and R_{2} = 20  k\Omega. In place of the ideal 796 pF capacitor, a standard-valued capacitor C = 800 pF can be used. The oscillation frequency would then be f_{o} = 19.9  kHz. Element tolerance values should also be considered.
Comment: As usual in any electronic circuit design, there is no unique solution.
Reasonably sized component values should be chosen whenever possible.
Computer Simulation Verification: A Computer simulation was performed using the circuit in Figure 15.18(a). Figure 15.18(b) shows the output voltage versus time.
Since the ratio of resistancesis R_{2}/R_{1} = 22/10 = 2.2,the overall gain is greater than unity so the outputincreases as a function of time. This increase shows the oscillation nature of the circuit. Another characteristic of the circuit is shown in Figure 15.18(c).
A 1 mV sinusoidal signal was applied to the input of R_{1} and the output voltage measured as the frequency was swept from 10 kHz to 30 kHz. The resonant nature of the circuit is observed. The oscillation frequency and the resonant frequency are both at approximately 18.2 kHz, which is below the design value of 20 kHz.

If the capacitor in the circuit is reduced from 796 pF to 720 pF, the resonant frequency is exactly 20 kHz. This example is one case, then, when the design parameters need to be changed slightly in order to meet the design specifications