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The following circuit shows a MOS Wilson mirror in which Q1 and Q3 are matched, and they have the same (W/L)1 ratio that is 2 times of the (W/L)2 of Q2. All MOSFETs have the same Vt. 1) Derive the relationship between lout and IREF 2) Using small-signal model of the MOSFETs, derive and appreciate the output resistance of the current source, Ro.

The following circuit shows a MOS Wilson mirror in which Q1 and Q3 are matched, and they have the same (W/L)1 ratio that is 2 times of the (W/L)2 of Q2. All MOSFETs have the same Vt. 1) Derive the relationship between lout and IREF 2) Using small-signal model of the MOSFETs, derive and appreciate the output resistance of the current source, Ro.

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The following circuit shows a MOS Wilson mirror in which Q1 and Q3 are matched, and they have the same (W/L)1 ratio that is 2 times of the (W/L)2 of Q2. All MOSFETs have the same Vt. 1) Derive the relationship between lout and IREF 2) Using small-signal model of the MOSFETs, derive and appreciate the output resistance of the current source, Ro.

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Figure P9.19 shows a MOS differential amplifer with the drain resistors RD implemented using diode-connected PMOS transistors, Q3 and Q4. Let Q1 and Q2 be matched, and Q3 and Q4 be matched. (a) Find the differential half-circuit and use it to derive an expression for Ad in terms of gm1,2, gm3,4, ro1,2, and ro3,4. (b) Neglecting the effect of the output resistances ro, find Ad in terms of μn, μp, (W/L)1,2 and (W/L)3,4. (c) If μn = 4μp and all four transistors have the same channel length, find (W1,2/W3,4) that results in Ad = 10 V/V.
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