Question

Figure 3: Common-source amplifier with a LC resonator load (a) Draw a small-signal equivalent circuit of a common-source amplifier with a resonant load in Fig. 3. Hint: You will end up with a parallel RLC resonator formed by RL, LD and CD at the drain node. (b) In (a), please prove that the small-signal voltage gain is given by AV = -gmZD, where ZD is the total impedance of the parallel RLC resonator at drain. Voltage gain in this case is defined as the ratio of input and output voltage phasors. (c) In (b), it follows that the magnitude of voltage gain is |AV| = gm |ZD|. ZD is the impedance of a parallel RLC resonator, so it is at its maximum at the resonant frequency f0 = 1/(2pisqrt(LDCD)). What is such maximum of |ZD|? Hint: At resonance, a parallel LC becomes an open circuit, leaving only the resistance.

          Figure 3: Common-source amplifier with a LC resonator load

(a) Draw a small-signal equivalent circuit of a common-source amplifier with a resonant load in Fig. 3. Hint: You will end up with a parallel RLC resonator formed by RL, LD and CD at the drain node.

(b) In (a), please prove that the small-signal voltage gain is given by AV = -gmZD, where ZD is the total impedance of the parallel RLC resonator at drain. Voltage gain in this case is defined as the ratio of input and output voltage phasors.

(c) In (b), it follows that the magnitude of voltage gain is |AV| = gm |ZD|. ZD is the impedance of a parallel RLC resonator, so it is at its maximum at the resonant frequency f0 = 1/(2*pi*sqrt(LDCD)). What is such maximum of |ZD|? Hint: At resonance, a parallel LC becomes an open circuit, leaving only the resistance.

Figure 3: Common-source amplifier with a LC resonator load

(a) Draw a small-signal equivalent circuit of a common-source amplifier with a resonant load in Fig. 3. Hint: You will end up with a parallel RLC resonator formed by RL, LD and CD at the drain node.

(b) In (a), please prove that the small-signal voltage gain is given by AV = -gmZD, where ZD is the total impedance of the parallel RLC resonator at drain. Voltage gain in this case is defined as the ratio of input and output voltage phasors.

(c) In (b), it follows that the magnitude of voltage gain is |AV| = gm |ZD|. ZD is the impedance of a parallel RLC resonator, so it is at its maximum at the resonant frequency f0 = 1/(2*pi*sqrt(LDCD)). What is such maximum of |ZD|? Hint: At resonance, a parallel LC becomes an open circuit, leaving only the resistance.

Added by Laura H.

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