Question 10.9: Objective: Compare the output resistance of the cascode MOSF...
Objective: Compare the output resistance of the cascode MOSFET current source to that of the two-transistor current source.
Consider the two-transistor current source in Figure 10.17 and the cascode current source in Figure 10.18. Assume I_{REF} = I_{O} = 100 µA in both circuits, λ = 0.01 V^{−1} for all transistors, and g_{m} = 0.5 mA/V.
The output resistance of the two-transistor current source is, from Equation (10.48(b)),
r_{o} = \frac{1}{λ I_{REF}} = \frac{1}{(0.01)(0.10)} ⇒ 1 M \Omega
For the cascode circuit, we have r_{o2} = r_{o4} = 1 M \Omega. Therefore, the output resistance of the cascode circuit is, from Equation (10.57),
R_{o} = \frac{V_{x}}{I_{x}} = r_{o4} + r_{o2}(1 + g_{m} r_{o4}) (10.57)
R_{o} = r_{o4} + r_{o2}(1 + g_{m} r_{o4}) = 1 + (1)[1 + (0.5 × 10^{−3})(10^{6})]
or
R_{o} = 502 M \Omega
Comment: The output resistance of the cascode current source is substantially larger than that of the basic two-transistor circuit. Since d I_{O} ∝ 1/R_{o}, the load current in the cascode circuit is more stable against variations in output voltage.
Design Pointer: Achieving the output resistance of 502 MΩ assumes the transistors are ideal. In fact, small leakage currents will begin to be a factor in actual output resistance values, so a value of 502 MΩ may not be achieved in reality.