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Testing Power Sources for Stability
Testing Power Sources For Stability
©Venable Industries All Rights Reserved
Page 1


VENABLE TECHNICAL PAPER # 1

Testing Power Sources for Stability

Abstract:

Recent advances in measurement technology have made it not only possible to
measure stability margins, but made it a quick and simple process. On power
sources with remote voltage sensing terminals, gain and phase margins can
usually be determined in a few seconds without even removing the cover. These
measurements can be made while the source is operating normally, supplying
power to the real load. In this way, the effects of the real load on stability margins
and power source performance can easily be determined. This paper will explore
the causes of problems when the power source is connected to the real load as
opposed to the resistive load normally used by the power source manufacturers
and how to specify and test the power source to avoid those problems.

How a Power Source Regulates Voltage

In order to understand how to effectively test power sources for stability, one needs to understand
what stability means and where the feedback loop is in a power source. Figure 1 shows a simplified
block diagram of a typical power source. The power source may have several outputs, but prime
consideration is given to the one around which the loop is closed.



Figure 1. Block Diagram of Power Source Feedback Loop

The POWER PROCESSING CIRCUITRY is the power-handling portion of the power source,
typically from the PWM terminal of a control IC to the regulated output. On one popular control IC,
the SG1524, this is from pin 9 of the IC to the output of the power source that is being regulated. We
call this portion the MODULATOR.

Testing Power Sources For Stability
©Venable Industries All Rights Reserved
Page 2
The ERROR AMPLIFIER is the op-amp which senses the value of the controlled output and compares
it to the reference voltage, together with its associated input network, feedback network, and bias
components. We call this the AMPLIFIER. Typically, the output voltage is scaled by a divider
network consisting of a resistor in the input impedance block and a bias resistor, and then compared to
a constant reference voltage. If the output voltage is too high, the inverting input of the op-amp will be
more positive than the non-inverting input, and the output of the op-amp will swing negative, reducing
the output of the modulator. The opposite happens if the output voltage is too low. For all reasonable
frequencies above DC, the gain of the amplifier is the ratio of the FEEDBACK IMPEDANCE to the
INPUT IMPEDANCE. The bias resistor does not enter into the AC gain calculation, since it carries no
AC current.

The FEEDBACK LOOP is the path through the input impedance, the error amplifier, the power
processing circuit, and back around to the input impedance. The gain around this loop is the product of
the gain of the amplifier and the gain of the modulator. If the gains are expressed in dB, the gain
around the loop is simply the sum of the gain of the amplifier (in dB) and the gain of the modulator
(also in dB), since dB is a log scale and you multiply by adding logarithms. When multiplying two
quantities that have magnitude and phase components, the magnitudes are multiplied and the phases
are added, so the phase shift around the loop is simply the sum of the phase shift of the amplifier and
the phase shift of the modulator. As you might have guessed, by expressing gain in dB we have made
graphic analysis very easy. When gain is expressed in dB, the gain around a feedback loop is simply
the sum of the gains of all the pieces of the loop, and the phase shift around a loop is simply the sum
of the phase shifts of all the pieces of the loop.

TRANSFER FUNCTION is another way of expressing the gain and phase shift of a block as a
function of frequency. A typical method of displaying a transfer function is the BODE PLOT, which is
a plot of log gain and linear phase versus log frequency.

How Remote Sensing Works

With remote sensing, an extra pair of wires is included in the cable between the power source and the
load, as shown in Figure 2. These wires are connected to the controlled output voltage at the load, then
routed back to the error amplifier inside the power source so that the voltage can be sensed by the
wires that carry negligible current. If the cable is long, there can be a substantial voltage drop in the
power-carrying wires.




Figure 2. Power Source Feedback Loop with Remote Sensing of Output Voltage



Testing Power Sources For Stability
©Venable Industries All Rights Reserved
Page 3
The problem is that the power-carrying wires also have resistance and inductance. To make matters
worse, most of the time there is a substantial amount of capacitance across each output at the load. The
resistance and inductance of the leads, coupled with the capacitance of the load, cause additional phase
shift that affects the stability of the feedback loop. This phase shift is not present during testing of the
power source, which is typically tested with resistive loads and short cables, and the extra phase shift
causes degradation of the stability margins. Oscillation of the feedback loop is a common occurrence
when remote loads are first connected.

Review of the Basics

What Phase Is

To understand how oscillation occurs, it is necessary to understand phase and amplitude of sine waves.
Figure 3a shows a sine wave of voltage, and Figures 3b through 3e show the same waveform lagging
90°, 180°, 270°, and 360° respectively.




Figure 3. Phase

Notice that when the waveform lags by 360°, it is impossible to distinguish it from the original.

What Amplitude Is

Amplitude is the size of the sine wave. Figure 4a shows a sine wave with larger amplitude, and Figure
4c shows a sine wave with smaller amplitude.

Testing Power Sources For Stability
©Venable Industries All Rights Reserved
Page 4


Figure 4. Amplitude

If a feedback loop is broken, and a sine wave signal is applied to the input of the loop, the signal will
come back multiplied by the loop gain. At low frequency there is gain around the loop, and the signal
will come back with a larger amplitude. At high frequency there is loss around the loop and a sine
wave will come back with smaller amplitude. There is some frequency at which a sine wave will come
back with exactly the same amplitude, and this frequency is known as the UNITY GAIN
FREQUENCY, or GAIN CROSSOVER.

What Frequency Is

Frequency is the number of cycles of a voltage waveform in a given period of time, usually one
second. Figure 5b shows a sine wave. Figure 5c shows a higher frequency sine wave, that is, one with
more cycles per second. Figure 5a shows a lower frequency sine wave, that is, one with fewer cycles
per second. The important aspect of frequency is that reactive elements change impedance with
frequency. It is this change of impedance with frequency which makes the various slopes of the Bode
gain curve.




Figure 5. Frequency






Testing Power Sources For Stability
©Venable Industries All Rights Reserved
Page 5
Stability Criteria

Bode Stability Criteria

Unconditionally Stable Systems. < > As noted earlier, when a signal is shifted 360° in phase, it cannot
be distinguished from the original signal. The phase shift around a feedback loop typically increases
with increasing frequency. At some frequency, there will be a point where the total phase shift around
the loop equals 360°. The gain around a feedback loop typically decreases with increasing frequency.
There will be some frequency at which the gain is 1, that is, a signal injected in a feedback loop will
return with exactly the same amplitude. If the phase shift around the loop is 360° at the same
frequency at which the gain is 1, the signal coming back around the loop will look exactly like the
signal injected into the loop initially. If this condition exists, and the feedback loop is closed, any
disturbance will progress around the loop and come back exactly in phase with unity gain, and the
feedback loop will oscillate.

In order to make a feedback loop stable, the gain must be less than unity when the phase shift is a total
of 360°, and the phase shift must be less than 360° when the gain around the loop is unity. Figure 6a is
a Bode plot of