analogue problems
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1.Q1The 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=6k and rm=6kAssuming that iN1=1mA and iN2=0A, what is the value ofvOUT in Volts?
Assuming that iN1=0A and iN2=1mA, what is the value ofvOUT in Volts?
Assuming that iN1=1mA and iN2=1mA, what is the value ofvOUT 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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2.Q2Your company has recently invented a new field effect transistor called
ExpFET, with the symbol and terminal voltage-current characteristics given
below.
iG=0
iD={0K(evGSVTVN1)ifvGS
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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=4V and R=2k, andthe ExpFET parameters are: K=1mA, VT=1V and VN=1V.
Given that vIN=0.5V, what is the value ofvOUT in Volts?
Given that vIN=2V, what is the value ofvOUT in Volts?
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What is the value ofvIN in Volts when vOUT drops to VS2?
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 ofvIN in volts when vOUTdrops to VS2? (Recall that for a MOSFET in
saturation: iD=K2(VGSVT)2
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.
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Again, the circuit parameters are: VS=4V and R=2k, and the ExpFETparameters are K=1mA, VT=1V and VN=1V.
Given that VIN=2V, what is the small-signal gain (voutvin) of this circuit?
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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3.Q3
The impulse response of a circuit is its response to a unit impulse, (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)=1(t) volt-seconds. That
is, vIN is a unit impulse at time t = 0. In thecircuit, L=5mH, R1=10, C=33nF and R2=10k. Note that since thiscircuit is driven by an impulse and there is no other source of energy, the
capacitor voltage and inductor current att = 0 will be zero.
(a) What is the value ofvR1(t) at t=0 in Volts (V)?
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(b) What is the value ofvR1(t) at t=0+ in volts (V)? Hint: Recall that
that 0+0(t)dt=1
(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.)
(d) What is the value ofvC(t) at t=0+ in volts (V)?
(e) What is the value for vC(t) at t=1ms in volts (V)?
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4.Q4
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In this problem we investigate the time response of the circuit shown below
which contains two switches S1and 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, R1R2, C, L, T and t, as applicable.
What is the expression for vC(t) during the time interval 0T?
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5.Q5The 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(j)=Vo(j)Vi(j)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.
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Transfer function H(j) magnitude plots
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Transfer function H(j) phase plots
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Which plot (A-F) corresponds to the magnitude ofH(j)=Vo(j)Vi(j) in the
above circuit?
Which plot (U-Z) corresponds to the phase ofH(j)=Vo(j)Vi(j) in the above
circuit?
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Which plot (A-F) corresponds to the magnitude ofH(j)=Vo(j)Vi(j) in the
above circuit?
Which plot (U-Z) corresponds to the phase ofH(j)=Vo(j)Vi(j) in the above
circuit?
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Which plot (A-F) corresponds to the magnitude ofH(j)=Vo(j)Vi(j) in the
above circuit?
Which plot (U-Z) corresponds to the phase ofH(j)=Vo(j)Vi(j) in the above
circuit?
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6.Q6This 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.
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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
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Assume that in the circuit
above, V0=5V, T=0.1ms, Rw=1, Lw=0.5mH and RL=4.
What is the time constant (in milliseconds) associated with the rise ofvoltage vR?
What is the time constant (in milliseconds) associated with the fall of
voltage vR?
What is the value ofVmax in Volts?
What is the value ofVmin in Volts?
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