Bode Plot Basic Concepts and Practical Applications

Bode plot is usually drawn as an asymptotic approximation as connected straight lines; the bending points of the Bode plot correspond to the 3-dB point of the actual amplitude transfer function, which is also at a pole or a zero.

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The slope of amplitude Bode plot for voltage or current is Nx20dB/dec;

The phase Bode plot approaches Nx90 degrees after every pole/zero.

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Left-hand-plane (LHP) zero improves phase margin, by bending up both magnitude and phase; example of LHPZ is Rgd-and-Cgd-in-series induced zero, as 1/((gm^(-1)-Rgd)*Cgd), where Rgd is larger than gm^(-1);

Right-hand-plane (RHP) zero worsens phase margin, by bending up magnitude but bending down phase; example of RHPZ is Cgd induced zero, as 1/(gm^(-1)*Cgd).

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How to determine the frequency of a pole or a zero from a transfer function in simulation?

1. Look at the amplitude transfer function and locate the bending points; this is very difficult, when poles and zeros are close to each other;

2. Look at the phase transfer function: if the phase curves bends down from 0 to -90 degrees, there is a pole at -45 degrees; similar to zeros;

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How to determine which circuit node contributes to a pole or zero? 

1. Add a cap at one circuit node and the other node of the cap is grounded; increases the cap value, and observe the moving of the corresponding pole in the Bode plot;

2. When there are two nodes having C or RC cross them, modifies C or RC values and observe the moving of the corresponding zero in the Bode plot;

3. For the case that the signal passes several circuit nodes, one can look at the transfer function across two circuit nodes step by step, starting from the circuit input. For example, if the signal passes node A(input), B and C(output), one can first simulate transfer function between A and B to get the pole/zero contributed by A and B, then simulate transfer function between A and C so that one can isolate the extra pole/zero contributed only from C;

One can disconnect the following node connections (e.g., disconnecting C from the circuit) when analyzing the previous circuit nodes (A and B), which help prevent the loading effects from following circuit nodes;

Poles contributed by input/output nodes can be obtained by simulating the input/output impedance, whose imag part is contributed by cap.

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The above assumes that the poles and zeros are real value;

for the case that poles/zeros pair are complex, amplitude Bode plot bends extra -/+40dB/dec, and there are peaking around such complex poles/zeros; the phase Bode plot bends to extra -/+180 degrees.

Q: Do you ever see the case of complex zeros in circuit design?

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References:
http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/Bode.html

http://wikis.controltheorypro.com/index.php?title=Bode_Plot

http://en.wikibooks.org/wiki/Control_Systems/Bode_Plots

Bode Plot Basic Concepts and Practical Applications