Feature: Analogue design
Producing control loop Bode plots Standard Bode plots yield three critical measurements, which can be used to determine stability and speed: • Phase margin; • Crossover frequency (bandwidth); and
• Gain margin. It is generally accepted that 45-60°
Figure 1: Switching regulator control loop Bode plot measurement with a network analyzer for (a) voltage regulator and (b) LED driver.
To make the measurement, the control loop is broken and a sinusoidal perturbation pushes into a high impedance path, while the resulting control loop gain and phase are measured, enabling the designer to quantify the stability of the loop
of phase margin is required for a stable system, and that -10dB gain margin is required for guaranteed loop stability. The crossover frequency relates to general loop speed. Figure 1 shows the setup for making these measurements using a network analyzer. LTspice simulation can be used
to create a similar injection and measurement in the control loop for an LED. Figure 2 shows an LED driver (LT3950) with an ideal sine wave of a given frequency injected directly into the feedback path on the negative sense line (ISN). Measurement points A, B and C are used to calculate the gain and the phase at the injection frequency. In order to graph the entire Bode plot, this measurement must be repeated over a large frequency range, stopping at fSW
/2 (half the converter’s switching
frequency). To make the measurement, the
control loop is broken and a sinusoidal perturbation pushes into a high impedance path, while the resulting control loop gain and phase are measured, enabling the designer to quantify the stability of the loop. Te measurement of points A, B
Figure 2: LT3950 DC2788A demonstration circuit LED driver LTspice model with control loop noise injection and measurement points
idea of control loop stability – a starting point for compensation component choices and output capacitor sizing. Te process of using LTspice based on
Middlebrook’s original recommendation in 1975 is well documented (see “LTspice: Basic Steps in Generating a Bode Plot of SMPS”). Te actual signal injection location laid out in Middlebrook’s method is not commonly used these days but has been adjusted over the years, resulting in
the injection location shown in Figure 1a. Furthermore, LED drivers, with high-
side sense resistors and complicated AC resistance LED loads, should have a different injection point than either today’s injection point or Middlebrook’s original recommendation, one not previously demonstrated in LTspice. Te method presented here generates LED driver current-sense feedback loop Bode plots in LTspice, and in the lab.
and C in Figure 2 determine the gain and phase of the control loop at the injection frequency. Different injection frequencies yield different gain and phase. For simplicity, and to see how this works, one can set the injection frequency and measure the gain and phase of A-C and B-C. Tis yields a single frequency point of the Bode plot. Figures 3a and 3b show the gain and phase of 10kHz ± 10mV AC injection. Figures 3c and 3d show the gain and phase of 40kHz ± 10mV AC injection. A sweep of frequencies and the measurements of gain and phase
www.electronicsworld.co.uk May 2022 27
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52
