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.