analogue problems

8/22/2019 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?


2/17

Assuming that Input 2 is left as an open circuit, what is the Thevenin

equivalent resistance (in kOhms) seen from Input 1?

You have used 0 of 3 submissions

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


3/17

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?


4/17

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?


6/17


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)?


4.Q4


8/17

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?


9/17


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.


10/17

Transfer function H(j) magnitude plots


11/17

Transfer function H(j) phase plots


12/17

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?


13/17


above circuit?


circuit?


14/17


above circuit?


circuit?


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.


15/17

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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