This document discusses Bode plots, which are used to analyze the frequency response of variable-frequency networks. Bode plots consist of two graphs: a magnitude plot using a logarithmic scale on the horizontal axis to show gain or attenuation over frequency, and a phase plot to show phase shift over frequency. Zeros cause positive gain slopes on the magnitude plot, while poles cause negative slopes. Phase is determined from the tangent inverse of the transfer function. Bode plots provide an efficient way to understand a network's behavior at different frequencies.

1. Circuit Analysis – II (EE-201)Variable-frequency Networks
Part 2

2. Sinusoidal Frequency Analysis
Bode plots to display frequency response data
VARIABLE-FREQUENCY NETWORK
PERFORMANCE
LEARNING GOALS

3. SINUSOIDAL FREQUENCY ANALYSIS
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5. Bode Plots
• These are Magnitude and Phase based pair of plots
• The Horizontal Access is always a logarithmic scale frequency (f or ꙍ)
• The vertical is a 20log(k + jꙍ) Magnitude plot in 1st part
• The vertical access is tan-1(jꙍ/k) Phase plot in 2nd part
• Most of the times, we take all k’s common from the tf and thus we use
1+jꙍ/k instead k+jꙍ,
• The common terms are multiplied with Constant gain portion so the overall
effect on the graph is none.
• It is calculated for a transfer function of
H(w) = Gain* Polynomial(Zeros)/ Polynomial( Poles)

6. Zeros, Poles and Gains
• The zeros are on the top of transfer function (tf) equation (numerators) so the
magnitude is positive elevation
• Poles are the denominator of tf equation so are negative depressions on graph
• Two polos or Zeros at the same value makes the elevation or depression doubled
• A pair of a pole and a zero cancels out the effect on graph
• When a pole or zero is already drawn, and a second pole or stars its effect, the
previous depression or elevation is effected and thus a composite plot is formed.
• Constant terms with H(w) such as Gains are straight lines with a fixed magnitude.
• We add up all gains, poles and zeros to get our overall plot

7. Drawing a Zero on Bode plot
• A zero has 20dB/decade elevation starting from its position.
• We always convert the zeros and poles to 1+jꙍ/k or 1+s/k form
• Before the value of s or jꙍ is reached on the x-axis, the 20log(1+jꙍ/k) is negligible because ꙍ is
small hence jꙍ/k is more small. Also 20log(1+0) is 0.
• If a zero is at origin, jꙍ=0, then it is a +20dB/decade increasing line, crossing ꙍ axis at 0
• It is an approximation and real plots may be more smooth due to continuous values.

8. Drawing a Pole on Bode plot
• A Pole has -20dB/decade depression starting from its position.
• We always convert the poles to 1+jꙍ/k or 1+s/k form
• Before the value of s or jꙍ is reached on the graph, the -20log(1+jꙍ/k) is negligible because ꙍ is
small jꙍ/k is more small. Also -20log(1+0) is 0.
• If a pole is at origin, jꙍ=0, then it is a -20dB/decade decreasing line, crossing ꙍ axis at 1
• Approximation encounters difference between plots

9. Drawing Phase in bode plot
• We calculate Phase by using tan-1(imaginary/real) method for individual terms in the tf.
• Phase of a constant term is 0 since the imaginary term in such case is zero.
• (jꙍ+0), jw=0 has a 90o phase, always, throughout the graph
• For zero, it is positive
• For pole it is negative
• jꙍ=k has a phase change of +90o or -90o between k and 10 x k
• If we consider a zero such as (1+jꙍ/k), the 0 to 90 degree phase inversion will start from k and will complete at 10k
• If we consider a pole such as (1+jꙍ/m), the 0 to -90 degree phase inversion will start from k and will complete at 10k
• The slope is 45o/decade

14. H(s) =

15. H(s) =

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