Question
Asked Feb 26, 2020
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In the circuit of Figure P6.9:
R = 1.3 k2
R2 = 1.9 k2
C = 0.5182 µF
Determine:
a. How the voltage transfer function
V.(jo)
V.(jo)
Hy(j») =
behaves at extremes of high and low frequencies.
b. An expression for the voltage transfer function and
show that it can be manipulated into the form
H.
H,(jo) =TFjf(@)
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In the circuit of Figure P6.9: R = 1.3 k2 R2 = 1.9 k2 C = 0.5182 µF Determine: a. How the voltage transfer function V.(jo) V.(jo) Hy(j») = behaves at extremes of high and low frequencies. b. An expression for the voltage transfer function and show that it can be manipulated into the form H. H,(jo) =TFjf(@)

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where
R2
H. =
f(ω) -
wR¡R2C
R + R2
R1 + R2
c. The frequency at which f(@) = 1 and the value of
H, in decibels.
1,(j) R,
I(ja)
ww
V(jo)
c+R V(ja)
help_outline

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where R2 H. = f(ω) - wR¡R2C R + R2 R1 + R2 c. The frequency at which f(@) = 1 and the value of H, in decibels. 1,(j) R, I(ja) ww V(jo) c+R V(ja)

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Expert Answer

Examination of the given circuit.

The circuit is shown below.

Electrical Engineering homework question answer, step 1, image 1

 

First, the transfer function will be determined in order to solve the first subpart. Once the value of the transfer function is calculated the other subparts can be subsequently determined.

(a) Calculation of the transfer function.

In the given circuit, the capacitor and the resistor are connected in parallel. First be calculate the equivalent impedance after that the voltage divider rule will be applied to calculate the output voltage, thus the value of the transfer function can be determined.

Electrical Engineering homework question answer, step 2, image 1

Electrical Engineering homework question answer, step 2, image 2

The output voltage is given as:

Electrical Engineering homework question answer, step 2, image 3

 

The transfer function of the given circuit is calculated, the behavior of the transfer function at low frequency is given as:

Electrical Engineering homework question answer, step 2, image 4

At low frequency, the transfer function comes out to be:

Electrical Engineering homework question answer, step 2, image 5

The behavior of the transfer function at low frequency is given as:

Electrical Engineering homework question answer, step 2, image 6

At very high frequency the transfer function comes out to be zero.

(b) Part

To proof that the transfer function can be represented in the form as:
Electrical Engineering homework question answer, step 3, image 1

 

The expression of the transfer function will be divided by the suitable parameters of the circuit to achieve the desired expression.

Electrical Engineering homework question answer, step 3, image 2

 

The above transfer function becomes.

Electrical Engineering homework question answer, step 3, image 3

 

...

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