Quote:
Originally Posted by G8HQP Dave
Your simplified model of the cascode will not enable you to derive the full equations you quoted; to do that you need to take account of everything which is going on.
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This remark made me look at how to derive the equation for the gain of Cascode quoted by Millman & Halkias. Actually I can derive it quite easily except for one aspect that was initially difficult (for me).
To be able to calculate the voltage gain for cascode it is necessary to know what the impedance is looking into the cathode of the upper device (once this is known its dead easy). The best way to do it is to use the principle that the impedance between two nodes in a circuit equals the open circuit voltage divided by the short circuit current.
Doing that, the upper device has an impedance of (rp+R)/(u+1) looking into the cathode. Which also shows how u effectively lowers the input impedance of the upper device.
Once this is known it is all downhill easy, because in the cascode circuit you can then replace the upper device by an impedance of (rp +R)/(u+1) and replace the lower device by a voltage generator u(Vin) in series with an impedance rp.
Hence the generator is u(Vin) and the total load is rp + (rp + R)/(u+1).
Then to calculate the output current it is uVin/(rp + (rp+R)/(u+1) ). Then, multiplying this current by the load resistance R to get Vout, yields their exact equation for Vout/Vin.