The basic design rules for power distribution networks (PDN) teach us that the best performance is obtained from a uniform, frequency independent (or flat) impedance profile. This is one reason that power supply stability is important, since a power supply with poor stability results in an impedance peak, which degrades the flat impedance profile and also the performance of the circuit being powered.
Since no impedance path is perfectly flat, we need to make some design adjustments. This article aims to help you make compromises that have the minimum impact on the system performance.
The source impedance should match the impedance of the transmission line.
This is a basic premise of S parameter measurements and of all RF equipment in general. The source impedance (most often 50Ω) is connected to a coaxial cable that has an impedance matching the source, and the load is terminated into the same impedance. This results in a perfectly flat impedance looking either from the source to the load or from the load to the source.
The output impedance of a voltage regulator can be considered to be a source while the PCB planes can be represented as a transmission line. The far-end decoupling capacitors are the load.
Transmission line basics
At frequencies below the resonant frequency of the transmission line, the characteristics of the transmission line can be defined by inductive and capacitive terms. The capacitance can be measured with the transmission line unterminated at the far end. The inductance can be measured with the transmission line shorted at the far end. The characteristic impedance of the transmission line can be determined from these two measurements as
The frequency at which the inductance and capacitance intersect is the characteristic impedance and is
A properly matched transmission line presents a perfectly flat impedance with a magnitude equal to the characteristic impedance. An improperly terminated transmission line is represented as capacitive or inductive and has many resonances and anti-resonances at multiples of the resonant frequency of the line. If the line is capacitive, then an anti-resonance occurs first. If the line is inductive, then a resonance occurs first. In both cases, the frequency of the first resonance or anti-resonance is
These relationships are shown using a 50Ω coaxial cable simulation in Figure 1. The unterminated end impedance is measured with an open, short and matched termination at the terminated end of the cable.
In the event that the transmission line and the source are not matched, there are two possible solutions depending on whether the termination resistance is greater than or less than the characteristic impedance. If the termination resistance is less than the transmission line characteristic impedance, then the anti-resonant peaks exceed the termination resistance. These impedance peaks are defined by
The resonant minima’s are equal to the termination resistance.
If the termination resistance is greater than the transmission line characteristic impedance, then the resonant peaks are equal to termination resistance. The anti-resonant minima’s are defined by
These relationships are shown using the previous simulation model with termination resistances of 24.9Ω 210Ω and are matched in Figure 2.
These relationships are confirmed in a measurement of a 50Ω coaxial cable terminated in 24.9Ω and 210Ω in Figure 3.
These concepts are extended to an actual printed circuit board with a SMA connector soldered at the center of a 4.5” x 6.3” bare copper clad, double-sided PCB as shown in Figure 4.
We can approximate the characteristic impedance of the PCB using the oscilloscope measurement in Figure 4. The capacitance is estimated using marker M3.
Alternatively, the characteristic impedance can be seen as the intersection of the open and shorted impedance, occurring at approximately 11.5dBΩ or 3.76Ω.
The characteristic impedance of the PCB can also be calculated using (4) and the approximate peak impedance (14.5dBΩ) with the 2.7Ω termination resistance.
The measurement is repeated using a termination resistor of 3.6Ω, as shown in Figure 5.
The PCB is simulated for comparison with Figure 5, and the results are shown in Figure 6.
Finally, a dynamic transient response is simulated at the PCB resonant frequency using a 0.6and 3.6Ω source impedance at the power supply. The simulation model is shown in Figure 7 and the simulation results are shown in Figure 8.
Conclusions
Several methods of determining the characteristic impedance of a circuit board have been demonstrated. Key relationships have been defined between the PCB characteristics and the PDN performance and using simulation models. After making actual measurements, the relationships are confirmed.
The determination of whether the PCB impedance is greater than the termination impedance, or conversely, if the termination impedance is greater than the PCB impedance, can be made by looking to see if the first artifact is a resonance or an anti-resonance.
These results clearly show why it is imperative to match the PCB planes to the output impedance of the regulator in order to optimize the PDN performance. It is desirable to have the PCB plane equal to the regulator output impedance, though if this is not possible, the PCB impedance should be LOWER than the regulator output impedance in order to better contain the peak excursion related to the peak impedance maxima.
