In the cross-coupled oscillator circuit shown in Fig. 15.1.1, $R_{p}$ represents the loss of each inductor. Each transistor is operating at a transconductance $g_{m}$ and has an output resistance $r_{o}$. Find the oscillation frequency $\omega_{0}$ and explain why the circuit oscillates at this frequency. Also, derive an expression for the minimum value of $g_{m}$ needed to obtain sustained oscillations.

Figure 15.1.1

Question

In the cross-coupled oscillator circuit shown in Fig. 15.1.1, $R_{p}$ represents the loss of each inductor. Each transistor is operating at a transconductance $g_{m}$ and has an output resistance $r_{o}$. Find the oscillation frequency $\omega_{0}$ and explain why the circuit oscillates at this frequency. Also, derive an expression for the minimum value of $g_{m}$ needed to obtain sustained oscillations.

Figure 15.1.1

Quizplus · Accepted Answer

The Answer of In the cross-coupled oscillator circuit shown in Fig. 15.1.1, $R_{p}$ represents the loss of each inductor. Each transistor is operating at a transconductance $g_{m}$ and has an output resistance $r_{o}$. Find the oscillation frequency $\omega_{0}$ and explain why the circuit oscillates at this frequency. Also, derive an expression for the minimum value of $g_{m}$ needed to obtain sustained oscillations.

Figure 15.1.1

In the Cross-Coupled Oscillator Circuit Shown in Fig RpR_{p}Rp​ Represents the Loss of Each Inductor

In the Cross-Coupled Oscillator Circuit Shown in Fig $R_{p}$ Represents the Loss of Each Inductor