Micrel, Inc.
MIC4720
Network
Analyzer
“A” Input
Loop Stability and Bode Analysis
Network
Analyzer
“R” Input
Bode analysis is an excellent way to measure small
signal stability and loop response in power supply
designs. Bode analysis monitors gain and phase of a
control loop. This is done by breaking the feedback loop
and injecting a signal into the feedback node and
comparing the injected signal to the output signal of the
control loop. This will require a network analyzer to
sweep the frequency and compare the injected signal to
the output signal. The most common method of injection
is the use of transformer. Figure 7 demonstrates how a
transformer is used to inject a signal into the feedback
network.
+8V
R1
1k
MIC922BC5
Output
Feedback
R3
1k
R4
1k
Network Analyzer
Source
50
Figure 8. Op Amp Injection
R1 and R2 reduce the DC voltage from the output to the
non-inverting input by half. The network analyzer is
generally a 50Ω source. R1 and R2 also divide the AC
signal sourced by the network analyzer by half. These
two signals are “summed” together at half of their
original input. The output is then gained up by 2 by R3
and R4 (the 50Ω is to balance the network analyzer’s
source impedance) and sent to the feedback signal. This
essentially breaks the loop and injects the AC signal on
top of the DC output voltage and sends it to the
feedback. By monitoring the feedback “R” and output
“A”, gain and phase are measured. This method has no
minimum frequency. Ensure that the bandwidth of the
op-amp being used is much greater than the expected
bandwidth of the power supplies control loop. An op-amp
with >100MHz bandwidth is more than sufficient for most
power supplies (which includes both linear and
switching) and are more common and significantly
cheaper than the injection transformers previously
mentioned. The one disadvantage to using the op-amp
injection method; is the supply voltages need to below
the maximum operating voltage of the op-amp. Also, the
maximum output voltage for driving 50Ω inputs using the
MIC922 is 3V. For measuring higher output voltages,
1MΩ input impedance is required for the A and R
channels. Remember to always measure the output
voltage with an oscilloscope to ensure the measurement
is working properly. You should see a single sweeping
sinusoidal waveform without distortion on the output. If
there is distortion of the sinusoid, reduce the amplitude
of the source signal. You could be overdriving the
feedback causing a large signal response.
Figure 7. Transformer Injection
A 50Ω resistor allows impedance matching from the
network analyzer source. This method allows the DC
loop to maintain regulation and allow the network
analyzer to insert an AC signal on top of the DC voltage.
The network analyzer will then sweep the source while
monitoring A and R for an A/R measurement. While this
is the most common method for measuring the gain and
phase of a power supply, it does have significant
limitations. First, to measure low frequency gain and
phase, the transformer needs to be high in inductance.
This makes frequencies <100Hz require an extremely
large and expensive transformer. Conversely, it must be
able to inject high frequencies. Transformers with these
wide frequency ranges generally need to be custom
made and are extremely expensive (usually in the tune
of several hundred dollars!). By using an op-amp, cost
and frequency limitations used by an injection
transformer are completely eliminated. Figure
demonstrates using an op-amp in a summing amplifier
configuration for signal injection.
8
M9999-051707
May 2007
14
MICREL [ MICREL SEMICONDUCTOR ]
