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In the circuit shown...

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Document Preview: 1A) 
 
In the circuit shown below, the input, x(t) versus output, y(t) is indicated graphically by  
two relations as illustrated. Suppose and x = sin(? t) where ? is a constant. (i) 
s  o o   
Sketch the discrete voltage spectrum of the output y(t) = v in each case and explain with 
o  
reason(s) for any type of distortion being present in the output (in each case) 
 
(Hint: Expand v and find the associated harmonic constituents) 
o

R 
s
Output 
Input
 y 
 
+ y(t) = k × x(t)

+ 
  
v = y(t) 
v = x(t) o  
in Network 
x (t) y(t) = k + k × x(t) +
s 
o  1  
2
k × [x(t)]
 
2  
 
x

1B) 
 
In the above problem, suppose and x = [C cos(? t) + C sin(? t)] where ? ? ; and C
s XXXXXXXXXX > 1 1  
and C are constants.(i) Sketch the discrete voltage spectrum of the output y(t) = v in 
2 o  
each case and explain with reason(s) for any type of distortion being present in the output (in 
each case) 
 
(Hint: (i)  Expand  v via superposition; (ii)  Use  the  trigonometric  relations:  sin(A  ±  B)  = 
o    
(sinAcosB ± cosAsinB) or  cos(A ± B) = (cosAcosB m  sinAsinB) as necessary and (iii) find the 
associated harmonic constituents)Input side Output side

Z  
s

+ v (t) 
L

Z 
 o

Z
in 
 
+ 
 
Z Load 
L  
 v (t) 
i
+ 
impedance 
v (t) 
s
v (t) 
o v = Av 
o in

Z : Input impedance 
 in
Z : output impedance 
o

Circuit with transfer 
function A 
 
In the above circuit, v (t) = v (t) × Z /(Z + Z ) = v (t)/(Z / Z + 1). If the source 
i s in s   in s s in   
impedance Z >> Z (or when ideally, Z ? 8), v (t) will be maximum, ? v (t). 
in s in i s
 
Similarly, v (t) = v (t)  ×  Z /(Z + Z ) =  v (t)/(Z / Z + 1);  and,  when  the  output 
L o L o L o o L    
impedance  Z

David · Accepted Answer

HERE ARE THE BASICS HELPFUL IN ALL THE PROBLEMS:-
Amplifier Gain of the Input Signal
Voltage Amplifier Gain
Current Amplifier Gain
Power Amplifier Gain
·  Voltage Gain in dB:    av  =  20 log Av
·  
·   Current Gain in dB:    ai  =  20 log Ai
·  
·   Power Gain in dB:      ap  =  10 log Ap
ANSWER 1 A)
Input x(t) = sin ωo t 
For y(t) = ko + k1 x(t) + k2[x(t)]^2
; y(t) = ko + k1 sin ωo t  + k2 sin^2  ωo t
; y(t) = ko + k1 sin ωo t  + k2 (1- cos 2  ωo t)/2
; y(t)= ko + k2/2 + k1 sin ωo t  - k2  cos 2  ωo t
Spectrum of the signal 
ANSWER 1 B);
; y(t)= ko + k1 x(t) + k2[ x(t)]^2
;  y(t) = ko + k1 C1  cos (ω1t) + k1 C2 sin(ω2 t) + k2 C1^2 cos^2ω1 t + k2 C2^2 sin^2ω2 t
;

Please see attachment and complete all problems. Document Preview: 1A) In the circuit shown below, the input, x(t) versus output, y(t) is indicated graphically by two relations as illustrated. Suppose...

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