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Implement a current source, with cascode topology, using Diodes Inc's 2N7002K MOSFET, satisfying the following requirements:

  1. Use a voltage source of 5.5 Volts
  2. \$ i_{out} = 6 ~ \mu A\$
  3. \$ V_{out_{min}} < 2.5 V \$
  4. \$ R_{out} > 0.7~G\Omega \$

Asume that the n-MOSFET has a \$\lambda= 104~\mu V^{-1}\$


My attempt:

schematic

simulate this circuit – Schematic created using CircuitLab

Here you can see the simulation (using an arbitrary \$150k\Omega\$ load), and the output current works fine. My concern is with the output impedance.

My question is how to compute the output impedance of this n-MOSFET current source?

I'm not sure if in this case I can use the (known) small-signal output impedance formula of a cascode configuration wich, according to Sedra-Smith, is \$ r_{out} \approx g_{m} r_{o_1}r_{o_2}\$, where \$r_{o_1}=r_{o_2}=r_o=\frac{1}{\lambda I_D} = \frac{1}{106\mu V^{-1}\times 6\mu A} = 1.6~G\Omega \$

My guess is that I can not use this formula, because my current source is a DC source (\$ \neq \$small signal) while this formula was deduced from the small-signal model.

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    \$\begingroup\$ Output impedance is a small signal parameter - it is the slope of the output. \$\endgroup\$ – Kevin White May 11 '17 at 4:11
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    \$\begingroup\$ My guess is that I can not use this formula Well, you can, at a certain point of operation the circuit behaves as an ideal current source (at the DC value of 6uA) in parallel with a resistor of 1.6 Gohm. That 1.6 Gohm is indeed the slope of the output voltage/current in the part where the current is nearly constant. \$\endgroup\$ – Bimpelrekkie May 11 '17 at 5:51

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