Q1
The circuit shown below is the linear equivalent model of a two-input single-output amplifier. Note that it contains a current
dependent voltage source.
One application of this amplifier is in a communications circuit where its two inputs are driven by two antennas. We can
model the two antennas as two current sources: iIN1 and iIN2, as shown below.
The elements in the circuit have the following values: R=9kΩ and rm=9kΩ
Assuming that iN1=1mA and iN2=0A, what is the value of vOUT in Volts?
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Assuming that iN1=0A and iN2=1mA, what is the value of vOUT in Volts?
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Assuming that iN1=1mA and iN2=1mA, what is the value of vOUT in Volts?
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Assuming that Input 2 is left as an open circuit, what is the Thevenin equivalent resistance (in kOhms) seen from Input 1?
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Q2
Your company has recently invented a new field effect transistor called ExpFET, with the symbol and terminal voltagecurrent characteristics given below.
iG=0
iD={0K⋅(evGS−VTVN−1)
if vGS<VTif vGS≥VT
iG=0
iD={0K⋅(evGS−VTVN−1)if vGS<VTif vGS≥VT
Your company believes that the ExpFET is superior to the MOSFET for certain applications. In particular, it believes that
when an ExpFET is used instead of a MOSFET in a standard inverter circuit, the output voltage drops more quickly as the
input voltage is increased. You are asked by your company to verify this belief using the standard inverter circuit shown
below.
The circuit parameters have the following values: VS=5V and R=2kΩ, and the ExpFET parameters are: K=1mA, VT=1V and
VN=1V.
Given that vIN=0.5V, what is the value of vOUT in Volts?
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Given that vIN=2V, what is the value of vOUT in Volts?
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What is the value of vIN in Volts when vOUT drops to VS2?
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Now you replace the ExpFET with a MOSFET with parameters K=1mAV2, and VT=1V.
Assuming the MOSFET is operating in the saturation region, what is the value of vIN in volts when vOUT drops to VS2?
(Recall that for a MOSFET in saturation: iD=K2(VGS−VT)2
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Your company also believes that the small-signal voltage gain (voutvin) of a common-source amplifier is higher when using
an ExpFET instead of a MOSFET. You are now asked to verify this using the common-source amplifier circuit shown below.
Again, the circuit parameters are: VS=5V and R=2kΩ, and the ExpFET parameters are K=1mA, VT=1V and VN=1V.
Given that VIN=2V, what is the small-signal gain (voutvin) of this circuit?
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Now you replace the ExpFET with a MOSFET with parameters K=1mAV2 and VT=1V.
Given that VIN=2V and assuming that the MOSFET is operating in saturation, what is the small-signal gain (voutvin) of this
circuit?
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Q3
The impulse response of a circuit is its response to a unit impulse, δ(t). Knowing the impulse response of a linear circuit is
extremely valuable as we can figure out the circuit's response to an arbitrary input from it. In this problem you will find the
response of a circuit when it is driven by a unit impulse.
Consider the circuit shown above in which vIN(t)=1δ(t) volt-seconds. That is, vIN is a unit impulse at time t = 0. In the
circuit, L=5mH, R1=10Ω, C=33nF and R2=10kΩ. Note that since this circuit is driven by an impulse and there is no other
source of energy, the capacitor voltage and inductor current at t = 0 will be zero.
(a) What is the value of vR1(t) at t=0− in Volts (V)?
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(b) What is the value of vR1(t) at t=0+ in volts (V)? Hint: Recall that that ∫0+0−δ(t)dt=1
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(c) What is the value for vR1(t) at t=1ms in volts(V)? (Hint: The L-R1 and C-R2 branches of the circuit are decoupled.)
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(d) What is the value of vC(t) at t=0+ in volts (V)?
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(e) What is the value for vC(t) at t=1ms in volts (V)?
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Q4
In this problem we investigate the time response of the circuit shown below which contains two switches S1 and S2.
Until time t=0, both switches are open and the circuit is initially at rest, i.e., vC(t=0−)=0 and iL(t=0−)=0. At t=0, switch S1
is closed but S2 stays open. After a VERY LONG time T, S1 is opened and S2 is simultaneously closed.
Answer the following questions in terms of the parameters: V, R1 R2, C, L and t, as applicable.
What is the expression for vC(t) during the time interval 0<t<T?
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What is the expression for vC(t) during the time interval t>T?
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What is the expression for iL(t) during the time interval t>T?
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Q5
The circuits in this problem are driven by sinusoidal sources and are in the steady state. For each circuit, enter the letter
corresponding to its magnitude and phase plot for the transfer funrction H(jω)=Vo(jω)Vi(jω) from the magnitude (A-F) and
phase (G-L) plots sketched in the figures below. The magnitude plots are on a log-log scale and the phase plots are on a
linear-log scale. Note these are sketches, look for correct approximate shape.
Transfer function H(jω) magnitude plots
Transfer function H(jω) phase plots
Which plot (A-F) corresponds to the magnitude of H(jω)=Vo(jω)Vi(jω) in the above circuit?
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Which plot (U-Z) corresponds to the phase of H(jω)=Vo(jω)Vi(jω) in the above circuit?
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Which plot (A-F) corresponds to the magnitude of H(jω)=Vo(jω)Vi(jω) in the above circuit?
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Which plot (U-Z) corresponds to the phase of H(jω)=Vo(jω)Vi(jω) in the above circuit?
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Which plot (A-F) corresponds to the magnitude of H(jω)=Vo(jω)Vi(jω) in the above circuit?
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Which plot (U-Z) corresponds to the phase of H(jω)=Vo(jω)Vi(jω) in the above circuit?
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Q6
This problem investigates how digital signals are distorted as they travel over real wires. A real wire is not a perfect short
circuit, instead it has resistance, inductance and capacitance. In this problem we assume that the wire has been designed to
have very low capacitance, so the capacitance can be ignored, and the wire can be modeled as shown in the figure below.
Here Rw and Lw model the series resistance and inductane of the wire. The voltage source vS(t) models the signal source
and RL is the resistance of the load where the signal is received. The signal source generates a square-wave voltage with
period 2T and maximum value V0, as shown below.
In steady state, the voltage signal measured across the load resistor appears as shown below
Assume that in the circuit above, V0=10V, T=1ms, Rw=2Ω, Lw=1mH and RL=3Ω.
What is the time constant (in milliseconds) associated with the rise of voltage vR?
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What is the time constant (in milliseconds) associated with the fall of voltage vR?
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What is the value of Vmax in Volts?
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What is the value of Vmin in Volts?