ECE3050 Assignment 111. The figure shows the ac signal circuit of a cascade common-source amplifier. For each MOS-FET, it is giv en that ID=2mA, r0= ∞,andK =0.25 × 10−3A/ V2. The circuit elementvalues are RS=1kΩ, RS1= RS2= 510 Ω, RD1= RD2=15kΩ.(a) Show that gm1= gm2=1.414 mS and rs1= rs2= 707.1 Ω.(b) Use the T models or simplified T models to show that the voltage gain is given byvovs=−RD1rs1+ RS1×−RD2rs2+ RS2= 152 (43.6dB)(c) Use the π models to show that the voltage gain is given byvovs=−RD11gm1+ RS1×−RD21gm2+ RS2= 152 (43.6dB)(d) Show that the input resistance is given b yrin= ∞(e) Show that the output resistance is giv en byrout= RD2=15kΩ(f) What would be the new gain if a resistor RL=1kΩ is connected from output to ground?Answ er: vo/vs=9.50 (19.6dB), a decrease of 24 dB.2. The ac s ignal circuit of a common-gate a mplifier driving a common-drain amplifier is shown.For each MOSFET, it is given that ID=2mA, r0= ∞,andK =0.5mA/ V2. The circuitelement values are RS1= 220 Ω, RD1=15kΩ, RS2=2kΩ.(a) Show that gm1= gm2=2mSand rs1= rs2= 500 Ω.(b) Use the T models or simplified T models to show that the voltage gain is given byvovs=RD1rs1+ RS1×RS2rs2+ RS2=16.67 (24.4dB)1(c) Use the π models to show that the voltage gain is given byvovs=RD11gm1+ RS1×RS21gm2+ RS2=16.67 (24.4dB)(d) Show that the input resistance is given b yrin= 500 Ωwhere Rtd1= RD1.(e) Show that the output resistance isrout= 400 Ω(f) What would be the new gain if a resistor RL= 300 Ω is connected from output to signalground? Answer: vo/vs=7.143 (17.1dB), a decrease of 7.36 dB.3. The figure show s a common-drain amplifier followed by a common-source amplifier. For eachMOSFET, it is given that ID=1.5mA, r0= ∞,andK =0.5mA/ V2. The circuit elementvalues are RG=10kΩ, R1=1MΩ, RS1=2kΩ, RS2= 470 Ω,andRD2=20kΩ.(a) Show that gm1= gm2=1.732 mS and rs1= rs2= 577.4 Ω.2(b) Use the T models or simplified T models to show that the voltage gain is given byvovs=R1RG+ R1×RS1rs1+ RS1×−RD2rs2+ RS2= −14.8(c) Use the π models to show that the voltage gain is given byvovs=R1RG+ R1×RS11gm1+ RS1×−RD21gm2+ RS2= −14.8(d) Show that the input resistance is given byrin=1MΩ(e) Show that the output resistance is giv en byrout= RD2=20kΩ4. The figure shows a common-drain stage driving a common-gate stage. For each MOSFET, itis given that ID=2mA, r0= ∞,andK =0.5 × 10−3A/ V2. The circuit element values areRG=1MΩ, RS=200Ω, RD2=20kΩ.(a) Show that gm1= gm2=2mSand rs1= rs2= 500 Ω.(b) Use the T models or simplified T models to show that the voltage gain is given byvovs=RD2rs1+ RS+ rs2=16.67(c) Use the π models to show that the voltage gain is given byvovs=RD21gm1+ RS+1gm2=16.67(d) Show that the input resistance is given byrin= ∞(e) Show that the output resistance is giv en byrout=
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