Objective: Calculate the small-signal voltage gain of an NMOS amplifier with an active load.

For the amplifier shown in Figure 10.40(a) the transistor parameters are: $λ_{n} = λ_{p} = 0.01 V^{−1} , V_{T N} = 1 V$ , and $K_{n} = 1 mA/V²$ . Assume $M_{1}$ and $M_{2}$ are matched and $I_{REF} = 0.5 mA$ . Calculate the small-signal voltage gain for load resistances of $R_{L} = ∞$ and 100 kΩ.

Question

Objective: Calculate the small-signal voltage gain of an NMOS amplifier with an active load.

For the amplifier shown in Figure 10.40(a) the transistor parameters are: [latex]λ_{n} = λ_{p} = 0.01 V^{−1} , V_{T N} = 1 V[/latex], and [latex]K_{n} = 1 mA/V²[/latex] . Assume [latex]M_{1}[/latex] and [latex]M_{2}[/latex] are matched and [latex]I_{REF} = 0.5 mA[/latex]. Calculate the small-signal voltage gain for load resistances of [latex]R_{L} = ∞[/latex] and 100 kΩ.

Accepted Answer

Since [latex]M_{1}[/latex] and [latex]M_{2}[/latex] are matched, then [latex]I_{O} = I_{REF}[/latex], and the transconductance is
[latex]g_{m} = 2 \sqrt{K_{n} I_{REF}} = 2 \sqrt{(1)(0.5)} = 1.41 mA/V[/latex]
The small-signal transistor conductances are
[latex]g_{o} = g_{o2} = λ I_{REF} = (0.01)(0.5) = 0.005 mA/V[/latex]
For [latex]R_{L} = ∞[/latex], Equation (10.101) reduces to

[latex]A_{v} = \frac{V_{o}}{V_{i}} = −g_{m} (r_{o} || R_{L} || r_{o2}) = \frac{−g_{m}}{g_{o} + g_{L} + g_{o2}} [/latex] (10.101)
[latex]A_{v} = \frac{−g_{m}}{g_{o} + g_{o2}} = \frac{−1.41}{0.005 + 0.005} = −141[/latex]

For [latex]R_{L} = 100 k \Omega (g_{L} = 0.01 mA/V)[/latex], the voltage gain is
[latex]A_{v} = \frac{−g_{m}}{g_{o} + g_{L} + g_{o2}} = \frac{−1.41}{0.005 + 0.01 + 0.005} = −70.5[/latex]
Comment: The magnitude of the small-signal voltage gain of MOSFET amplifiers with active loads is substantially larger than for those with resistive loads, but it is still smaller than equivalent bipolar circuits, because of the smaller transconductance for the MOSFET.

Question 10.13: Objective: Calculate the small-signal voltage gain of an NMO...

Related Answered Questions

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

Objective: Calculate the small-signal voltage gain of an amplifier with an active load and a load resistance RL. For the circuit in Figure 10.37(a), the transistor parameters are VAN = 120 V and VA P = 80 V. Let VT = 0.026 V and ICo = 0.2 mA. Determine the small-signal voltage gain for load ...

Verified Answer:

Objective: Calculate the open-circuit voltage gain of a simple BJT amplifier with an active load. Consider the circuit shown in Figure 10.29. The transistor parameters are VAN = 120 V and VA P = 80 V. Let VT = 0.026 V ...

Verified Answer:

Objective: Compare the variation in bias current between the two- and three-transistor current-source circuits as a result of variations in β. A PSpice analysis is used. Figure 10.6(a) shows the two-transistor PSpice circuit schematic and Figure 10.6(b) shows the three-transistor PSpice circuit ...

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer: