How physics relates signal integrity, power integrity, and EMC

There came a time when high-speed electronic circuits reached speeds that required engineers to analyze the design for signal integrity (SI), power integrity (PI), and electromagnetic compatibility (EMC). Prior to that time, dedicated experts in separate teams focused primarily on their main specialty. The result: lengthy product review cycles when subsequent teams from these disciplines requested and implemented improvements that were actually bad for the others. When these teams started to cooperate more tightly and coordinated the reviews to find common solutions, commonalities and differences emerged, all rooted in the same basic physics laws. Here’s why.

At first glimpse, you may not realize the common thread in the three sketches in Figure 1. The left (a) shows a transmission-line symbol. The middle (b) shows a fraction of a schematic, potentially depicting two components on a power-distribution network (PDN). The right (c) shows a satellite communications example. Basic physics tells us that you can view all three in the context of characteristic impedance and propagation delay.

Signal Integrity Perspective

SI engineers are familiar with the fundamental equations that describe the Z₀ characteristic impedance and t_pd propagation delay of uniform interconnects. If we ignore losses, these equations became a function of per-unit-length inductance (L) and per-unit-length capacitance (C) of the transmission line.

The center schematic snippet may represent the simplified impedance of a DC source (R₁ and L) and a bulk capacitor (C and R₂) in the frequency range where the DC source becomes inductive, and the bulk capacitor’s impedance flattens out. PI engineers would know that if we want a smooth transition between the two impedances, we need to ensure the following:

We also know that the f_c resonance frequency between the capacitor and inductor is:

Though this is just a one-port lumped circuit, we can notice that (3) and (4) have essentially the same form of expressions as (1) and (2).

We may also wonder what is the corresponding item in Figure 1a to R₁ and R₂ in Figure 1b? Figures 2 and 3 explain and illustrate the connection. In short, when R₁ and R₂ in (3) are the same, they represent what we may call the lumped characteristic impedance of this circuit, making the impedance of the circuit frequency independent, just as terminating a lossless transmission line with its characteristic impedance makes its input impedance frequency independent.

Figure 2 shows the input impedance magnitude of a lossless 50-Ω transmission line with 2.5 ns propagation delay with different values of load resistance (R_load). At low frequencies, where the transmission line is electrically very short, the input impedance magnitude equals the load resistance. At higher frequencies, we notice the familiar periodic fluctuation of the input impedance. Notice the logarithmic frequency scale that compresses the sinusoidal variation as a function of frequency. As the load resistance approaches the characteristic impedance, the impedance peaks and valleys come closer and eventually, when the load resistance equals the characteristic impedance, the curve becomes a straight line. This shows what SI engineers know well: terminating the transmission line with its characteristic impedance eliminates reflections over a wide range of frequencies.

Power Integrity Perspective

Figure 3 illustrates how this relates to PI. We use the schematics from Figure 1 to look at the combined impedance of the parallel-connected R₁–L and C–R₂ network. The component values on the left illustrate potentially a medium-power DC source (this is the R₁–L leg) interacting with the bulk capacitor, represented by the C–R₂ leg. We vary only one component value, R₂, which in this example represents the equivalent series resistance (ESR) of the capacitor.

On the impedance plot in Figure 3, the black line represents the R1–L leg, the red lines show the impedance of the C–R₂ leg for the three C–R₂ values (short dashed line: R₂_max, solid line R₂_nom, long-dashed line: R₂_min) and the blue lines represent the combined impedance magnitude for the three R₂ values. We can see that when R₁ equals R₂ (and it also equals the

L/C = 10 mΩ value), the impedance magnitude plot becomes frequency independent, similar to the input impedance of a matched-terminated lossless transmission line. Another similarity is that pushing R₂ lower than the optimum value required for flatness actually creates an impedance peak at the LC resonance frequency.

To make the connection between the SI and PI illustrations in terms of cutoff frequency and propagation delay as well. Figure 4 and Figure 5 compare the frequency-domain and time-domain behavior of two circuits: a transmission line with Z₀ = 10 mΩ and t_pd = 1 µs propagation delay. For this, take the SI illustration circuit from Figure 2 and rerun that simulation with the characteristic impedance, LC values, and relative load impedance steps around 10 mΩ nominal value. Though a transmission line with 10 mΩ characteristic impedance is not practical for our typical signaling tasks, it matches the component values in our PI example in Figure 3.

Figure 5 shows the result of using extreme termination and looking at the response with fast step excitations. We take the transmission lines from Figure 2 and the equivalent transmission line from Figure 4 and apply a fast voltage source with a 0 V to 1 V swing.

Both waveforms show a damped periodic square-wave ringing, where the period of the ringing equals four times the propagation delay: 10 ns for the 50-Ω transmission line and 4 µs for the transmission line approximating the power circuit. (The 4x multiplier comes from the well-known quarter-wave resonator structure, since we have low impedance at one end and high impedance termination at the other end.)

Another way to view these circuits is to stay with the lumped circuit equivalent of the power circuit. The 10 nH inductance and 100 µF capacitor could be considered as the inductance and capacitance of a single-lump LC approximation of a transmission line. This leads us to the schematics shown on the left of Figure 6. We use the same source and load conditions we used on Figure 5: 1 mΩ source resistance and 100 mΩ load resistance.

From these figures, we can summarize that the lowest resonance frequency in a distributed transmission line occurs at the quarter-wave resonance:

The resonance resonant? frequency of the lumped LC circuit from Figure 6 was given in (4). Though the constant in the formula is slightly different, both expressions rely on the square root of the LC product.

EMC Perspective

Recall that Figure 1 includes an EMC case, where electromagnetic waves travel through a dielectric medium, most often through free space. In free space, we cannot speak about the medium’s capacitance and inductance. Instead, we can look at the permittivity and permeability material constants, which are proportional to capacitance and inductance when conductors form terminals. The permittivity of free space is ε₀ = 8.85 pF/m, and the permeability of free space is µ₀ = 4π × 10^-7 H/m. If we substitute L and C with these material constants and units, we get the very familiar results: the 120π= 377 Ω impedance of free space (in the far field) and the inverse of the speed of light: c = 3 × 10⁸ m/s.

Summary

From these examples, I’ve shown how the three disciplines — SI, PI, and EMC — are related. Even though they were introduced at different times and were motivated by seemingly different practical concerns, they share the same roots. PI engineers tend not to think about reflections during the design of lumped power distribution circuits. SI people tend to think of interconnects as conductor-bound distributed transmission lines, even though their behavior can also be described using lumped expressions. EMC people consider electromagnetic waves bouncing around in space. You can see how propagating waves connect transmission lines and lumped circuits through basic formulas. Once you understand their common roots, you can appreciate that distance along the signal propagation comes with finite delay and can be associated with inductance, no matter which discipline you look at. You can also see that the lumped equivalent circuit of a power distribution network can relate to reflections, commonly used in the context of transmission lines. Knowing these common roots helps you make more effective and better designs.