Magnetic components, transformers, capacitors emitting noise, excessive DC ripple, output voltage oscillation, overheating of power devices... These issues encountered during power supply R&D and design are often caused by unstable control loops. The Bode plot tells you how to solve them!

Why measure the loop?

As one of the important means to verify the stability of control systems, loop analysis finds its application in many scenarios. In switching power supplies and operational amplifier feedback networks, loop testing can clearly and accurately measure the stability and response speed of switching power supplies, providing electronic engineers with intuitive data references for designing stable control circuits. The measurement method of loop analysis can significantly reduce the verification cycle for loop stability and features intuitive waveform curve displays for easy observation and analysis.

Figure 1 AC-DC Switching Power Supply Topology Diagram

Principle of loop analysis testing

Loop analysis can be performed using either frequency sweep or single-frequency point testing. The principle of sweep frequency testing primarily involves injecting a sinusoidal signal with varying frequency into the switching power supply circuit, measuring the characteristics of the power supply in the frequency domain. By analyzing the crossover frequency, gain margin, and phase margin, the stability of the loop can be determined. Additionally, a Bode plot can display the system's gain magnitude and phase at different frequencies. During product development, engineers often need to repeatedly modify and debug the circuit. At this stage, loop analysis provides intuitive data comparisons, enabling quick determination of whether the system has reached a stable state and boosting engineers' confidence in product design!

Figure 2 ZDS4000/3000 Series Loop Analysis Interface

Loop Analysis Test Steps

1. Establishing the Loop Analysis Test System To perform the corresponding control loop tests, a disturbance signal (a swept sine wave signal within a certain amplitude and frequency range or a single-frequency sine wave signal) needs to be injected into the feedback path of the control loop. This feedback path refers to the resistive voltage divider network formed by R1 and R2. Additionally, a very small injection resistor must be inserted into the feedback loop to introduce an error signal. As shown in Figure 3.1, the injection resistor is labeled as 5Ω. Compared to the combined impedance of R1 and R2 in series, this injection resistor is negligible, so users may consider this low-value injection resistor as a permanent test component. Furthermore, an isolation transformer is required to isolate the AC disturbance signal, thereby avoiding any DC offset.

The test signal wiring is as shown in Figure 3.1. The oscilloscope controls the signal generator to output the required frequency signal, which is then injected across the injection resistor after passing through an isolation transformer. The oscilloscope uses a probe with X1 attenuation ratio for synchronous testing, and a grounding spring is preferred over a grounding clip whenever possible.

Figure 3.1 Loop Test Signal Wiring

2. After completing the wiring, we need to configure the key parameters for loop testing on the ZDS4000/3000 series oscilloscope:

Injection Channel: Refers to the channel connected to the injection reference signal, using this channel as the frequency reference for the current setting;

Output channel: refers to the channel connecting the feedback output signal;

Measurement options: selectable gain-phase, impedance-phase, amplitude-phase, and THD-phase;

Measurement Mode: Selectable between sweep or single-point;

Minimum Frequency: The minimum frequency value for sweeping, with a sweep range minimum selectable from 10Hz to 20MHz;

Maximum Frequency: The maximum frequency value for sweeping, with a sweep range maximum selectable from 100MHz to 30MHz;

Filter Enable: Whether to enable digital filtering during sweeping;

Filter Type: When filtering is enabled, either low-pass or band-pass filtering can be selected;

Cutoff frequency/Center frequency: Frequency settings for low-pass or band-pass filtering.

Points per decade: Sets the number of frequency points output by the signal generator module per decade in logarithmic scale, for example, the number of points between 100Hz and 1KHz.

Output voltage: Sets the peak-to-peak output voltage of the signal generator module.

Output impedance: Sets the output impedance of the signal generator module, which needs to match the impedance of the circuit under test.

Segment amplitude: When set to ON, the amplitude can be adjusted for each decade point within the current sweep range. If set to OFF, a uniform amplitude is applied throughout.

Figure 3.2 Parameter Setting Interface

3. Begin Testing

After confirming the settings are correct, initiate the test by pressing the [Run/Stop] button on the oscilloscope panel or clicking the [Start/Stop] button in the menu. Once the test starts, the interface will switch to the loop frequency sweep operation screen. This screen continuously and automatically plots dynamic curves of frequency vs. phase and frequency vs. gain based on the currently sampled frequency, phase difference, and gain. It also automatically adjusts the vertical display scale according to the curve range. The blue curve represents the gain curve, while the orange curve represents the phase curve, as shown in Figure 3.3.

Figure 3.3 Sweep Test Operation Interface

Result Analysis

Through the Bode plot of the sweep frequency curve, the trends of gain and phase changes across the entire frequency range can be visually observed. The gain margin (GM) and phase margin (PM) information are displayed in the upper right corner of the sweep interface. The phase margin (PM) refers to the phase value when the gain crosses 0 dB, while the gain margin (GM) is the gain value when the phase crosses 0°. PM and GM are important indicators for assessing the stability of switching power supplies.

Figure 4 Measured Sweep Curve

Through the final sweep curve

How to determine if a system is stable?

1. Crossover frequency (frequency at which gain is 0dB): Recommended to be 5% to 20% of the switching frequency;

2. Phase margin (phase at which gain is 0dB): Must be greater than 45°, recommended between 45° and 80°;

3. Crossover slope (near 0dB): Requires single-pole crossover, generally aiming for a slope around -1, i.e., -20dB/decade;

4. Gain margin (difference in gain when phase is 0°): Recommended to be greater than 10dB (note, GM is positive, while the measured gain value is negative, gain margin = 0dB – measured value).