UNIVERSITY OF CALIFORNIA AT BERKELEYCollege of EngineeringDepartment of Electrical Engineering and Computer SciencesEE105 Lab ExperimentsPrelab 7: Frequency ResponseName:Lab Section:v1(t)ACi(t)v2(t)Figure 1: Amplifier with a “Miller” capa citorThe Miller effect plays an important role in determining the poles of an amplifier. If there is a gain Aacross the capacitor C as shown in Figure 1, the current across C can be wr itten as:i(t) = Cddt(v1(t) − v2(t)) = Cddt(v1(t) − Av1(t))By distributing the derivative, this simplifies to:i(t) = C(1 − A)ddtv1(t)Therefore, the equivalent capacitance looking into v1(t) is the capacitance C multiplied by (1 − A). If thegain A is large enough, this Miller effect ca n make the capacitor dominate and contribute to the dominantpole of the amplifier. Using this same method, you can derive the equivalent capacitance looking into v2(t),which is C(1 − 1/A).1. For the common emitter amplifier shown in Figure 2, use the Miller approximation to derive the ex-pressions for the two poles of vout/vinin terms of Cµ, Cπ, gm, RS, rπ, and ro. These express ions willhelp you predict and understand the results of the lab.12−+VBIAS−vin+RSVCC= 5 VRC0.25 mAvOU TFigure 2: Common emitter amplifierωp1=ωp2=2. If RS= 51 Ω, RC= 10 kΩ, Cµ= 11 pF, Cπ= 25 pF, gm= 3 mS, rπ= 10 kΩ, and ro= 1 00 kΩ, whatare the poles of this amplifier?ωp1=ωp2=3. What will happen to the poles if a capacitor CMis added across the base collector junction?4. SPICE• Construct the common emitter amplifier circ uit shown in Figure 2 in SPICE. Use VBIAS= 0.58 V,RS= 51 Ω, and RC= 10 kΩ.• Use the 2N4401 SPICE model provided on the cour se website.• Perform an AC analysis of the circuit from 100 Hz to 10 GHz in HSPICE.3• Use Awaves to generate Bode plots (both magnitude and phase) for the circuit for vout/vin.Attach the Bode plots to this prelab worksheet. Do the results agre e with your hand calculations(check the pole frequencies
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