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Prof. Chris Toumazou
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Second generation SI cell
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E416 Spring 2007-set 1
Suggested problems Current mirrors and switched currents
1. Calculate the frequency dependence of the input impedance of a sourcedegenerated common source amplifier. Use this result to calculate the frequency
dependence of the small signal input impedance of the Wilson current mirror. It
may help to do the analysis as feedback problem rather than a circuit problem.Please remember the current input is meant to be driven by a vanishing
admittance current source!
2. Calculate the DC current gain error for matched BJT transistors for the simplecurrent mirror. Include the Early Effect. Use this result to infer the small signal
current gain error of the MOS simple current at a finite frequency, if you know
theT
f of the process. Remember the finite frequency current gain of a MOS
transistor is imaginary, i.e. incurs a 90 degree phase lag.
3. Calculate symbolically the small signal power gain of a simple BJT mirror at afinite frequency.
4. Calculate the harmonic distortion of a class A FET simple current mirror if theAC signal amplitude is equal to the bias, and if the AC signal amplitude is half the
bias, both at a finite frequency. Note that in strong inversion the gate-source
capacitance is essentially constant, so that the circuit IS NOT linear-time
invariant!
5. Calculate symbolically and plot the I-V characteristic of a diode connected (gate-drain connected together) FET, for:
a. A long gate FET: ( ) ( )2 12
DS L GS T DS
WI K V V V
L=
b. A short gate FET: ( )1.501.5
DS S GS T DS
WI K V V V
L=
c. In weak inversion: ( ) ( )/ /1GS T DSq V V nkT qV kT DS WI M e eL
=
For the purposes of this exercise you may assume 210 /LK A V= ,
1.510 /S
K A V= , 100M nA= , 0.3TV V= , .01= and .05 = . What is the gm
of each case? What are the typical impedance levels encountered?
6. Observe that a second generation switched current memory cell is equivalent to asimple current mirror driven by the signal masked by the switching waveform.
Use the results form Q3 above, the Convolution theorem and Power conservation
to estimate the gain error as a function of switching and signal frequency,provided the signal frequency satisfies the Nyquist criterion.
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