Power supplies are an important part of any electronic system. Older designs used to use linear power supplies. However, linear power supplies have a lot of power loss. Modern designs use switching DC-DC converters for power supplies. The main advantage of the switching DC-DC converters is that they have very high efficiency compared to linear power supplies.
All power supplies have input impedance, output impedance, reverse transfer impedance, PSRR. Loop stability is another important parameter for a power supply. Test and measurement of these parameters are of utmost importance in power supply design.
Input and output impedance of a power supply require DC biased impedance measurement. Measuring impedances in the range of ohms is easier with good accuracy. The real measurement challenge comes into play when we need to measure very low impedances, in the range of milli and micro ohms. Various factors need to be studied to perform high fidelity low impedance measurements. Ultra-low impedance measurements are commonly performed in high performance microprocessor power distribution network (PDN) designs. Vector network analysers (VNAs) are the main component used to measure ultra-low impedances due to their superior sensitivities. VNA has sensitivities in the order of microvolts and utilising two port shunt through measurement methods we can measure milli ohms and micro ohms. The two-port shunt through measurements are an adaptation of four wire kelvin measurements used for DC resistance measurements. Two port shunt through measurement comes with an inherent ground loop problem. Mitigating these are essential in measuring low impedances. Low impedance measurements in the range of micro ohms are impacted by the noise floor of the VNA and the cable shield resistances. Choosing the right methods, we can measure ultra-low impedances.
The power supply rejection ratio (PSRR) is a parameter that shows the capability of an operational amplifier (opamp) to minimize the effect of noise appearing in the opamp’s power supply pins without reflecting it on its output pins. It is defined as the ratio of change in supply voltage to the change in output observed. This is measured by adding a small sinusoidal voltage with the DC input to the opamp. Sometimes, it is also shown as 1/PSRR = dVOS/dVs, where VOS is the offset voltage and VS is the supply voltage [p.241, 1]. This is explained as the change in VOS brought by about 1V change in VS. In general, a higher PSRR means that the opamp is less sensitive to the supply variations. Some data sheets use separate PSRR ratings for each power supplies (+ve and -ve) used in the opamps marked as PSRR+ and PSRR- with respect to ground.
For a linear regulator powering a sensitive circuit, the PSRR is an important parameter. It shows that how well the regulator can filter out the power supply noise. The PSRR is measured without decoupling capacitors, otherwise, the capacitors will filter out the noise and the measured values will not be the true behaviour of an amplifier. Nowadays, it is becoming an important parameter for switching regulators as well due to their increased usage in point of load (PoL) applications. Switching regulators are preferred due to their higher efficiencies compared to their linear counterparts which suffers from efficiency losses.
They are important for voltage references too. PSRR is a significant performance concern as even small amounts of high frequency ripple voltage at the input can significantly degrade the output precision of voltage reference and impact downstream circuitry. For an analog to digital converter (ADC), PSRR is classified into DC and AC. PSRR DC is a measure of the offset error and is a static change. PSRR AC is a measure of the time varying signal’s PSRR. The output of a circuit is not just a function of the inputs, but also of the power supply, and so PSRR is an important parameter to be measured in many of these applications.
Like common mode rejection ratio (CMRR), PSRR is also often represented in dB since their magnitudes are often large. Both PSRR and CMRR degrades with frequency. Like CMRR, the PSRR measurement also must be performed for a range frequency. Usually, the CMRR of an opamp is in the range of 80 dB to 120 dB.
Methods to measure the PSRR in a practical circuit is provided in [1]. Reverse transfer impedance also can be measured with a VNA with a similar approach.
Stability is an important topic in power electronic switching converters. An unstable control loop result in oscillations in the output supply. An ideal voltage would be critically damped to avoid the oscillations. A step load response is taken as the final word on the converter stability. However, traditional stability assessment uses bode plots as a tool during design.
Bode plots represent the frequency response of a system. Bode plot is the gain and magnitude of a system as a function of frequency. Bode plot is widely used in power electronics to design control loops to estimate the converter stability. Accurate stability measurement is critically important to all power supply designs.
Bode plots include two plots – gain and phase plots. The gain and phase margin are plotted on Y axis as a function of frequency. They are plotted in logarithmic scale. Gain margin (GM) is the safety margin by which the open loop gain of a system can be increased without instability. This is given as GM = 20 log10(1/GH(e^(i*wp*T)) where wp is the phase cross over frequency. Phase margin (PM) is defined as PM in degrees = 180 + angle(GM(e^(i*wg*T)) where wg is the gain cross over frequency which is defined as the frequency at which the loop gain becomes one.
Measuring Bode plots are important part of DC-DC converter design. They can be measured using oscilloscope and a signal generator. Oscilloscopes like Tektronix 5 series, Tektronix 6 series, and Rohde & Schwarz RTM 3004 comes with in built function generators known as arbitrary function generator (AFG). Using these scopes and an injection transformer like Picotest J2100A or J2101A, we can easily obtain bode plot of a converter.
Bode plots became the traditional measurement for assessing control loop stability due to their simplicity. However, Bode plots fail when the control loop has multiple loops, and is not a fool proof method in modern switching converters. Many examples can be found in cases where the Bode plots fail and is well understood within the control system fraternity. Whenever Bode plots fail, it is important to assess the stability using Nyquist plots. Refer to http://www.cds.caltech.edu/~murray/books/AM05/pdf/am08-complete_22Feb09.pdf for Bode plots limitations. Nyquist plots contain the same information that is contained in the Bode plots. Nyquist plots can be generated from the measurement values obtained from Bode plots. Stability margin is the shortest distance between the Nyquist plot and the point (1,0). Picotest developed the NISM (Non-Invasive Stability Measurement) to solve the inherent issues of Bode plot without compromising simplicity which is based on the concepts of Nyquist plot. An added advantage is that NISM does not require breaking the control loop which is essential in obtaining Bode plots. All the difficulties are hidden from the user by the underlying mathematics and is programmed into the NISM for R&S ZNL6 VNA. NISM software can be downloaded from Picotest website.
