DC-DC Converter Loop Gain Measurement

1. Background and measurement methods

    The DC-DC converter can be viewed as a simple feedback control system, as shown in Figure 1.

Figure 1 A DC-DC converter can be abstracted as a feedback system

    For a negative feedback loop, the closed-loop gain is:

    When GH=-1, self-excitation will occur (GH is called open-loop gain). It can be decomposed into:

                    Amplitude condition: |GH|=1

                    Phase condition: GH phase Φ = -180º

    The open-loop characteristic is a very important parameter that characterizes the stability of the feedback system and is usually expressed in terms of gain margin and phase margin:

                   Gain margin: 0-Gain (dB) when Φ=-180°

                   Phase margin: When Gain=0, Φ-(-180º)

    It is usually represented by a Bode diagram as follows:

Figure 2 Open-loop gain of negative feedback system

    When testing the open-loop characteristics, the switching power supply should operate in a closed-loop state to ensure the stability of the system state.

Figure 3 Loop gain test connection diagram

    The output of the switching power supply is added with an electronic load; the input of the error amplifier is connected to the R port of the network analyzer E5061B through the high-impedance passive probe of the oscilloscope; the output of the switching power supply is connected to the T port of the E5061B through the high-impedance probe of the oscilloscope; the low-frequency LF output port of the E5061B is added to the input of the error amplifier and the output of the switching power supply through a transformer.

    The R port is used to measure the signal injected into the loop, and the T port is used to measure the output signal of the loop. T/R is the open-loop characteristic of the loop. To ensure the accuracy of the measurement, a through calibration is required before the test (normalization with Mem data is sufficient).

    In order to effectively inject RF energy into the DUT, the impedance of the transformer cannot be significantly lower than the impedance of the E5061B low-frequency LF output port (50 ohms); the transformer cannot have a resonance point within the test frequency range and should exhibit inductive properties to effectively inject the signal.

    The low frequency LF output signal of E5061B should not be too large or too small. If the signal is too small, all it measures is noise, and if it is too large, the feedback loop will be saturated. The signal size depends on the transformer, and the saturation depends on each switching power supply, so there is no fixed value.

    The excitation power can be changed during measurement, and an appropriate excitation power can be determined by looking at T/R, T, and R.

    Test results read:

    A. Usually it is measured under full load, half load and zero load conditions;

    B. Phase should be read under unwrap

    C. Gain margin: the loop gain when the phase of T/R is 0.

       Phase margin: The phase value when the loop gain is 0dB.

Figure 31 Loop gain reading

    As shown in the figure above: the phase margin is 67.4º at 580Hz (line A); the gain margin is 38.1dB at 18.6KHz (line B). The reading method of the gain margin and phase margin at this time is slightly different from that introduced in the principle part. The reason is that when measuring, the error amplifier (not just the GH) is included in the T/R, and there is a 180-degree reverse change.

2. Measuring instruments and accessories

    The instrument used to measure the loop gain of the DC-DC converter is: E5061B. The E5061B has a 1Mohm input impedance interface specially designed for this application, so that it can be directly connected to the oscilloscope passive probe for testing; the test frequency range of the DC-DC converter loop gain is: 5Hz to 30MHz, which meets various test requirements; it also supports impedance measurement and can measure the milliohm output impedance of the PDN; the 30ohm semi-floating design ensures measurement accuracy at low frequencies.

    A 1:1 transformer is required for testing. You can use: the transformer provided by Agilent (5188-4425); or the 0017CC transformer from North Hills; or the J2100A 5MHz or higher frequency transformer from Picotest.

    The complete configuration for testing the loop gain of a DC-DC converter is as follows:

    1.E5061B

       Options: 005, 3L5

    2. N2873A (2 required)

      5188-4425

      One BNC cable

    If you want to test the output impedance, you also need to add: 2 BNC cables, 1 11667L BNC power divider (for testing the low-frequency output port, frequency 5Hz-30MHz); 2 N(m)-SMA(f) conversion heads, 2 SMA-SMA coaxial cables, and 1 set of 85033E calibration parts (for testing the high-frequency output port, frequency up to 3GHz).