Bode plots represent the frequency response of a system. Bode plot is the gain and magnitude of a system as a function of frequency. Bode plot is widely used in power electronics to design control loops to estimate the converter stability. Accurate stability measurement is critically important to all power supply designs. Bode plots became the traditional measurement for assessing control loop stability due to their simplicity.
Bode plots include two plots – gain and phase plots. The gain and phase margin are plotted on Y axis as a function of frequency. They are plotted in logarithmic scale. Gain margin (GM) is the safety margin by which the open loop gain of a system can be increased without instability. This is given as GM = 20 log10(1/GH(e^(i*wp*T)) where wp is the phase cross over frequency. Phase margin (PM) is defined as PM in degrees = 180 + angle(GM(e^(i*wg*T)) where wg is the gain cross over frequency which is defined as the frequency at which the loop gain becomes one.
Measuring Bode plots are important part of DC-DC converter design. They can be measured using oscilloscope and a signal generator. Oscilloscopes like Tektronix 5 series, Tektronix 6 series, and Rohde & Schwarz RTM 3004 comes with in built function generators known as arbitrary function generator (AFG). Using these scopes and an injection transformer like Picotest J2100A or J2101A, we can easily obtain bode plot of a converter.
It is important to note that bode plot does not always predict stability accurately. Bode plots fail to predict stability when the control loop is of higher order. Refer to http://www.cds.caltech.
