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TDFS Impedance Stability of Transmission Line Fed LED Driver - Switching

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This example demonstrates the use of the TDFS method (Time Domain Frequency Sweep) to measure impedance stability ratio. The system is a switching DC/DC step-down power converter used for LED lighting, supplied by a battery through a long power cable.The TDFS impedance stability measurement model applies a 0.2A sinusoidal stimulus current at the point where the cable connects to the converter. The voltage at that point, as well as the stimulus current splits (toward the source and the load) are measured, and the associated source and load impedances vs. frequency are computed.The ratio of the source to load impedance is the impedance stability ratio (Tm). Similar to the open-loop frequency response requirement for closed-loop stability, Tm must not have magnitude = 1.0 at phase = 180 degrees, at any frequency.For this system, with a cable length of 400 meters and 8 AWG wire, the results show that the impedance ratio magnitude (green waveform) reaches unity (0 dB) at close to 2 kHz, where the phase (light blue waveform) is approximately 165 degress. This implies a "phase margin" of only 15 degrees, For a longer cable, this margin is further reduced. As shown in the companion example, "Transmission Line Fed LED Driver - Switching", for the cable length = 800 meters the system is unstable.This instability is the result of the "source" impedance (which includes the cable) variation over frequency, interacting with the varying load impedance. Note that at low frequency, the load effectively has a negative impedance, due to the constant power nature of the DC to DC converter.

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Description

This example demonstrates the use of the TDFS method (Time Domain Frequency Sweep) to measure impedance stability ratio. The system is a switching DC/DC step-down power converter used for LED lighting, supplied by a battery through a long power cable.

The TDFS impedance stability measurement model applies a 0.2A sinusoidal stimulus current at the point where the cable connects to the converter. The voltage at that point, as well as the stimulus current splits (toward the source and the load) are measured, and the associated source and load impedances vs. frequency are computed.

The ratio of the source to load impedance is the impedance stability ratio (Tm). Similar to the open-loop frequency response requirement for closed-loop stability, Tm must not have magnitude = 1.0 at phase = 180 degrees, at any frequency.

For this system, with a cable length of 400 meters and 8 AWG wire, the results show that the impedance ratio magnitude (green waveform) reaches unity (0 dB) at close to 2 kHz, where the phase (light blue waveform) is approximately 165 degress. This implies a "phase margin" of only 15 degrees, For a longer cable, this margin is further reduced. As shown in the companion example, "Transmission Line Fed LED Driver - Switching", for the cable length = 800 meters the system is unstable.

This instability is the result of the "source" impedance (which includes the cable) variation over frequency, interacting with the varying load impedance. Note that at low frequency, the load effectively has a negative impedance, due to the constant power nature of the DC to DC converter.

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Copy of TDFS Impedance Stability of Transmission Line Fed LED Driver - Switching - on Sun, 03/21/2021 - 11:01

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Description

This example demonstrates the use of the TDFS method (Time Domain Frequency Sweep) to measure impedance stability ratio. The system is a switching DC/DC step-down power converter used for LED lighting, supplied by a battery through a long power cable.

The TDFS impedance stability measurement model applies a 0.2A sinusoidal stimulus current at the point where the cable connects to the converter. The voltage at that point, as well as the stimulus current splits (toward the source and the load) are measured, and the associated source and load impedances vs. frequency are computed.

The ratio of the source to load impedance is the impedance stability ratio (Tm). Similar to the open-loop frequency response requirement for closed-loop stability, Tm must not have magnitude = 1.0 at phase = 180 degrees, at any frequency.

For this system, with a cable length of 400 meters and 8 AWG wire, the results show that the impedance ratio magnitude (green waveform) reaches unity (0 dB) at close to 2 kHz, where the phase (light blue waveform) is approximately 165 degress. This implies a "phase margin" of only 15 degrees, For a longer cable, this margin is further reduced. As shown in the companion example, "Transmission Line Fed LED Driver - Switching", for the cable length = 800 meters the system is unstable.

This instability is the result of the "source" impedance (which includes the cable) variation over frequency, interacting with the varying load impedance. Note that at low frequency, the load effectively has a negative impedance, due to the constant power nature of the DC to DC converter.

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Description

This example demonstrates the TDFS (Time Domain Frequency Sweep) Loop Stability Instrument Model. It is used to compute the open-loop transfer function of an operating (closed-loop) switching power converter. There is no need for state-average or continuous equivalent models for the modulator section of the design, as normally needed for frequency-domain (or "AC") analysis. Rather, the actual circuit component models can be used directly, because the open-loop transfer function is computed from time-domain simulation results.

In this case, the converter is operating at 200kHz switching frequency, and is converting the 12V DC input to a regulated 5V output, while supplying a 5A current to the 1 Ohm load resistor. The TDFS measurement instrument indicates that the open-loop gain crossover frequency is at 26 kHz, and the phase margin is just under 60 degrees. This verifies that the opamp-based lead-lag compensator is providing adequate stability margin under these operating conditions.

Note that the TDFS instrument model characterizes the open loop transfer function by injecting a small sinusoidal stimulus signal in series with the loop, and then measures the complex ratio of the return signal to the injected signal, is described in:

D. Venable, “Testing Power Sources for Stability”, Venable technical paper #1, Venable Industries.

The companion example, "Step-Down (Buck) DC to DC Converter - Switching", shows the line and load transient response of this converter design. Another companion example, "Step-Down (Buck) DC to DC Converter - Continuous", uses a state-average model of the switching (or modulator) section of the converter, so it supports traditional "AC" or frequency-domain analysis.

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