ECE3050 Homework Set 81. The figure shows the ac signal circuit of a cascade common-emitter amplifier. For each BJT,it is given that IE=1.5mA, α =0.99, β =99, rx=20Ω, r0= ∞,andVT=0.025 V.Thecircuit element values are RS=1kΩ, RE1= RE2=47Ω, RC1= RC2=10kΩ.(a) Looking out of the base of Q2, use the Norton collector circuit of Q1to show thatvtb2= −ic1Rc1= −134.03vsRtb2= RC1=10kΩ(b) Use the Norton collector circuit for Q2to show thatvo= 8097vsrout= RC2=10kΩ(c) Show thatrin= rib1=6.387 kΩ(d) If a resistor RL=1kΩ is connected from output to ground, show that the new gain isreduced by a factor RL/ (rout+ RL) to the value vo/vs= 736.1 and that the dB decreasein gain is 20.83 dB .2. The ac signal circuit of a common-base amplifier driving a common-collector amplifier isshown. For each BJT, it is given that IE=1.5mA, α =0.99, β =99, rx=20Ω, r0= ∞,and VT=0.025 V. The circuit element values are RS=50Ω, RC=10kΩ, RE=1kΩ. ??1(a) Looking out of the base of Q2use the Norton collector circuit of Q1to show thatvtb2= 148.06vsRtb2=10kΩ(b) Use the simplified T model for Q2to show thatvo=132.56vsrout= rie2kRE= 104.638 Ω(c) Use the simplified T model for Q1to show thatrin= rie1=16.867 Ω(d) If a resistor RL=1kΩ is connected from output to ground, show that the new gain isreduced by the factor RL/ (rout+ RL) to the value vo/vs= 120.01 and the dB decreasein gain is 0.864 dB. Note that the gain does not change nearly as much as it did inproblem 1. Explain.3. The figure shows a cascade common-collector amplifier, also called a Darlington connection.For each BJT, it is given that α =0.99, β =99, rx=20Ω, r0= ∞,andVT=0.025 V.The emitter current in Q2is IE2=10mA. The circuit element values are RS=10kΩ andRE= 100 Ω.(a) Looking out of the base of Q2,usethesimplified T model for Q1to show thatvtb2= vsRtb2= rie1= 350.2 Ω(b) Use the simplified T model for Q2to show thatvo=0.942vsrout= rie2kRE=5.84 Ω(c) Show thatrin= rib1=1.052 MΩ(d) If Q1and Q2are removed and REis connected to the right node of RS, show thatvo/vs=9.901 × 10−3, a decrease of 39.56 dB.4. The figure shows a common-collector stage driving a common-base stage. For each BJT, it isgiven that IE=1.5mA, α =0.99, β =99, rx=20Ω, r0= ∞,andVT=0.025 V. The circuitelement values are RS=1kΩ, RE= 100 Ω, RC=10kΩ.2(a) Use the simplified T model for Q1to show thatvte2= vsRte2= RE+ rie1=126.87 Ω(b) Use the Norton collector circuit of Q2to show thatvo=68.88vsrout= RC=10kΩ(c) Show thatrin= rib1=13.37
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