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ECE3040 — Assignment 5
- The figure shows the ac signal circuit for a combination common-source and common-drain amplifier.
(a) Replace the MOSFET with its pi model. Assume that r 0 = ∞. Show that vos vtg
gmRts 1 + gmRts
vod vtg
−gmRtd 1 + gmRts Note that one gain is positive and the other is negative. If Rts = Rtd, the gains are equal but of opposite signs. In this case, the circuit is called a “phase inverter.” (b) Replace the MOSFET with its T model. Assume r 0 = ∞. Show that vos vtg
Rtd rs + Rts
vod vtg
−Rts rs + Rts
(c) Show that the answers are equivalent.
- A common-drain amplifier followed by a common-source amplifier is shown.
(a) Replace the MOSFETs with the pi models and show that vo vtg 1
gm 1 (r 01 kRts 1 ) 1 + gm 1 (r 01 kRts 1 ) × gm 2 × [− (r 02 kRtd 2 )]
(b) Replace the MOSFETs with the T models and show that vo vtg 1
r 01 kRts 1 rs 1 + r 01 kRts 1
×
rs 2
× [− (r 02 kRtd 2 )]
(c) Show that the two answers are equivalent.
- The figure shows a common-drain amplifier followed by a common-gate amplifier. The small- signal models of the n-channel and the p-channel devices are identical.
(a) Assume that r 0 = ∞. Replace the MOSFETs with the pi models and show that gm 1 vgs 1 = −gm 2 vgs 2 , vtg 1 = vgs 1 + gm 1 vgs 1 RS − vgs 2 , and vo = −gm 2 vgs 2 Rtd 2. Solve these equations to obtain vo vtg 1
gm 1 1 + gm 1 RS + gm 1 /gm 2 × Rtd 2
(b) Assume that r 0 = ∞. Replace the MOSFETs with the T models and show by inspection that vo vtg 1
rs 1 + RS + rs 2 × Rtd 2
(c) Show that the answers are identical and explain which model makes this problem the simplest to solve.
- The figure shows a common-source amplifier. It is given that V +^ = +20 V, V −^ = −20 V, K = 0.0015 A/ V, VT H = 1.75 V, r 0 = 40 kΩ, RI = 200 Ω, R 1 = 1 MΩ, R 2 = 213.7 kΩ, RD = 7.2 kΩ, RS = 1.6 kΩ, and RL = 600 Ω.
(a) Show that ID = 2.5 mA and VDS = 18 V.
(c) If RI = 50 Ω, show that the new gain is Av = 13. 24.
- The figure shows the ac signal circuit of a common-gate amplifier with body effect. Assume that r 0 = ∞.
(a) Replace the MOSFET with its pi model and show that
vo vts
(gm + gmb) RD 1 + (gm + gmb) Rts
To show this, first show that vgs = −vs, vbs = −vs, vs = (gm + gmb) vgsRts + vts and that i^0 d = (gm + gmb) vgs. (b) Replace the MOSFET with its T model and show that
vo vts
RD
rskrsb + Rts
where rs = 1/gm and rsb = 1/gmb. (c) Show that the two answers are identical.
