SummaryProblem - The addition of an input filter to a switching-mode power supply can cause the combination to go unstable and oscillate. The Bode plot of the voltage-loop gain may not indicate a problem even at the onset of instability for current-programmed converters. Relevance - Adding an input filter to a switching-mode power supply or installing it in a system with an EMI filter can degrade its performance or cause it to go unstable. Long input cables or added output capacitance may cause the same problems. Solvability - To quickly determine if there is a problem, a graphical technique for duty-ratio programmed converters known as the Middlebrook Criterion is used. The criterion has been expanded to current-programmed converters by Jang and Erickson. Solution - For optimum design, the switching-mode power supply and the input filter or EMI filter should be designed together using criteria developed for this purpose. The criteria for both voltage-programmed and current-programmed converters is in a paper by Jang and Erickson. Personal - A personal anecdote. On the Web - Additional information on the Web. References - Key papers including a timeline.
ProblemDegradation. In addition to sustained oscillations or underdamped ringing, other performance parameters of the regulator can be degraded, especially the output impedance of the regulator. Source. Certain source and line impedances can cause similar problems. For example, the inductance of a long input power cable, interacting with a capacitance on the input of the switching mode power supply can cause ringing and oscillation. Load. Adding capacitance to the load can also cause the problem. Sustained Oscillation Characteristics Amplitude. The sustained output voltage oscillations due to input-filter interactions can have an amplitude of up to twice the input voltage of the converter, but is usually less. Frequency. The frequency is near the resonant frequency of the input filter. Example. For example, a 5 Volt regulator operating from a 28 V battery with an LC input filter whose resonant frequency is 1 kHz, could have a 56 Volt peak-to-peak one kHz sinusoidal oscillations on the 5-volt output, however it is usually less, e.g. 5 volts peak-to-peak (0 to 10 V peak). Cause. The cause of the oscillation is the negative input resistance characteristic of switching-mode regulators or other constant-power devices. Negative Resistance Input Characteristic Transformer Model. A simple model of a switching-mode power supply is to consider it a dc transformer with the turns ratio u. Input voltage Vin is u*Vout and the input current Iin is (1/u)*Iout. However, the input resistance Rin is not the output resistance u^2*Rout but is -u^2*Rout. The negative sign comes from the constant power characteristics of a switching-mode regulator as is shown in the derivation: Derivation. dVin d P P Vin Vout
Rin = ---- = ---- --- = - ------- = - --- = -u^2 ----
dIin dIin Iin Iin^2 Iin Iout
= -u^2*Rout
More sophisticated derivations in the references take into account efficiency and other regulator characteristics such as the frequency range over which the input impedance is negative. Do not use this information for design without independent verification of the information. Editor: Jerrold Foutz |
