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ELECTRIC CIRCUIT THEORY

Outline
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3
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5
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Node, loop and cut-set analysis of linear networks
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Frequency response of networks
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Periodic non-sinusoidal currents and linear circuits
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1

Frequency response of networks
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In other words, given the input signal amplitude, phase, and frequency,
knowledge of the frequency response of a circuit permits the computation
of the output signal

2

Frequency response of networks
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To express the frequency response of a circuit in terms of variation in
output voltage as a function of source:
Let
𝑉𝐿 (𝑗𝜔)
𝐻𝑉 𝑗𝜔 =
𝑉𝑆 (𝑗𝜔)

3

Frequency response of networks
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𝑍𝐿
𝑉𝐿 =
𝑉𝑇
𝑍𝐿 + 𝑍𝑇
𝑍𝐿
𝑍2
=
𝑉𝑆
𝑍𝐿 + (𝑍𝑆 + 𝑍1 )𝑍2 Τ(𝑍𝑆 + 𝑍1 + 𝑍2 ) 𝑍𝑆 + 𝑍1 + 𝑍2
𝑍𝐿 𝑍2
=
𝑍𝐿 𝑍𝑆 + 𝑍1 + 𝑍2 + (𝑍𝑆 + 𝑍1 )𝑍2
4

Frequency response of networks
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If the phasor source voltage and the frequency response of the circuit are
known, the phasor load voltage can be computed as follows:
𝑉𝐿 𝑗𝜔 = 𝐻𝑉 𝑗𝜔 ∙ 𝑉𝑆 𝑗𝜔
𝑉𝐿 𝑒 𝑗∅𝐿 = |𝐻𝑉 |𝑒 𝑗∠𝐻𝑣 ∙ 𝑉𝑆 𝑒 𝑗∅𝑆

Or

𝑉𝐿 𝑒 𝑗∅𝐿 = |𝐻𝑉 |𝑉𝑆 𝑒 𝑗(∠𝐻𝑣 +∅𝑆 )

5

Frequency response of networks
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Both |𝐻𝑉 | and ∠𝐻𝑣 are function of frequency
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Filtration systems are used to eliminate impurities from drinking water and
Sunglasses are used to filter out eye-damaging ultraviolet radiation and
reduce the intensity of sunlight reaching the eyes
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e
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Type of Filter
• Low-pass filters
• High-pass filters
• Bandpass Filters, Resonance, and Quality Factor

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Low-pass filter
A simple RC filter and denotes its input and output voltages respectively,
by 𝑉𝑖 and 𝑉𝑜
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12

High-Pass Filters
Just as you can construct a simple filter that preserves low frequencies and
attenuates higher frequencies
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Consider the circuit shown in

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