Power Supply Instability (1 of 3) |
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Causes of power supply instability and methods to prevent it occurring in manufacturing and field use.
Problem
The power supply can operate in different modes, such as the continuous and discontinuous current mode, presenting different control loop parameters in each mode. The input voltage can appear in the gain of the feedback loop, changing the gain characteristics as the input voltage swings over the wide operating range typical of many applications. Load variations affect the location of poles or zeroes associated with the output filter. The effective value of components contributing to poles and zeros, such as inductors and the load resistance, can vary as a function of line and load variations. The circuit can contain both real and complex right-half-plane zeroes that migrate as a function of line, load, and temperature. Many of the components affecting circuit poles and zeroes are nonlinear, such as swinging inductors. Many of the components affecting stability have large variations in tolerance as purchased and over operating temperatures and system life, such as electrolytic capacitors. Long power source leads or added system filters, such as EMI filters can have a dramatic effect on system stability criteria. See Input Filter Interaction. Added load capacitance, including high quality decoupling capacitors shorting the ESR of the power supply output capacitor, which may be contributing a stabilizing zero, can effect stability. Minor loops inside the power supply, like those causing emitter follower oscillations or power MOSFET drive resistance instabilities, may go unstable over the range of purchasing tolerance or variations caused by manufacturing, temperature, and age. These can go unstable with little noticeable effect on output observables (except perhaps radiated EMI in the Megahertz range), but can alter the feedback loop by causing saturation of components or DC level shifts in interior states and can greatly degrade field reliability. Things like the magnetizing current in the magnetics can affect stability. Switching noise can affect stability and stability measurement. One of the industries first challenges with switching-mode power supplies was trying to measure small gain and phase signals in a noise environment much larger than the signal. See personal anecdote below. Chaos can occur in these circuits. See Chaos and personal anecdote below.
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Simple Switching Power Supply Topologies (7 of 7) |
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One easy way to turn our prototype buck converter into a 5 V regulator is to sense the output and turn the switch on when the voltage is less than 5 V and turn the switch off when the voltage is greater than 5 V. This form of control is called by various names including bang-bang control, ripple regulators, and hysteretic control. It is instructive to exam this operation in the state-plane. For the following plots the values of L and C are the same (75 uH and 1200 uF) but load is one ohm instead of 0.25 ohm (less damping shows the effects better). |
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Simple Switching Power Supply Topologies (6 of 7) |
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The state-plane, sometimes called the phase-plane, is a plot with two state-variables as coordinates. State-variables are variables whose initial conditions are required to determine the future behavior of the system. Typically they are anything that stores energy, like inductors and capacitors, or anything with a memory, such as a flip-flop. Common state-planes in switching-mode power supply design are inductor current versus capacitor voltage in the output LC filter (approximates load current and load voltage), the derivative of capacitor voltage (approximates the inductor current without the dc component) versus capacitor voltage, and the derivative of the output capacitor voltage versus the voltage (you do not have to be concerned with any currents and the derivative always crosses the voltage axis at right angles). Trajectories are unique for a set of initial conditions and never cross each other. Trajectories in the state-plane can easily be determined by most SPICE programs that are used to determine the time response of a circuit. |
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Simple Switching Power Supply Topologies (5 of 7) |
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First let's turn on the switch and watch what happens to the output voltage versus time. For illustrative purposes we want the filter under-damped so we will decrease the load by increasing the load resistor from 0.25 ohms to 1.0 ohms. |
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Simple Switching Power Supply Topologies (4 of 7) |
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From our parts list we will add a capacitor to our switched inductor converter and get the buck converter as shown in Figure 3-5. 
Figure 3-5: Buck Converter
The buck converter goes by many names, voltage step-down converter, current step-up converter, chopper, direct converter, et .al. No matter the name, converters derived from this topology account for a substantial percentage of all converters sold. Understanding its operation is basic to switching-mode power supply design. Our first problem is to select initial values of L and C. Later the design can be optimized. In our switched inductor example we used the rule of thumb of designing L to get a peak-to-peak ripple current of 10% of the full load output current and got a value of 75 uH. We will use overshoot to get a value for C and then check the output ripple. |
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