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# Impedance Matching in Interconnects with Inductive Circuit Loads Each of these traces act like an inductive circuit

Your circuit diagrams are extremely useful for getting a basic idea of how your circuit behaves and how a signal will interact with a load component. In reality, an interconnect and a load component can behave as a purely resistive, purely capacitive, or purely inductive circuit, depending on geometry and the behavior of different components in the circuit. Here’s what you need to know about working with an inductive circuit in a PCB and how to ensure signal integrity.

## Every Interconnect is a Capacitive and Inductive Circuit

One dirty secret that you won’t normally hear in an introductory electronics class is this: every interconnect is really an RLC circuit. This is because every circuit is arranged with conductors in a loop, it has some residual inductance. In a PCB, the magnetic permeability of your substrate material and the geometry of your conductors will determine the inductance of your circuit. Similarly, because portions of conductors between a source and a load are separated by some dielectric (again, the PCB substrate), a circuit also has some parasitic capacitance.

In a typical circuit diagram and a schematic, these parasitics are not present in an ideal circuit as they depend on how a real circuit is laid out. Whether this significantly affects the behavior of your circuit depends on a number of factors, including the geometry of your circuits and the behavior of the load and source components. One can attempt to model the behavior of a real circuit using a circuit diagram by including an inductor in series between the source and load, as well as a capacitor between the high potential line and ground. This is essentially the way a lumped transmission line model is constructed; an example is shown below. Circuit model for a real trace connected to a load component (Z).

This circuit model shows a real model for a trace and a load component with impedance Z. You can find the definition of each parameter from the standard lumped transmission line model. At DC voltage, the trace is purely resistive, i.e., only the resistance of the copper trace and the conductance of the substrate (normally taken as G = 0) determine losses on the traces. As frequency increases above 0 Hz, a trace starts behaving as an inductive circuit, meaning the trace impedance increases as a linear function of frequency. Eventually, the capacitive nature of the substrate takes over at higher frequencies and balances the inductive nature of the trace, and the impedance saturates at the typical transmission line value.

## Resistive, Capacitive, and Inductive Circuit Elements and Devices

So what does this mean for the behavior of signals on an interconnect? The answer depends on whether we are dealing with digital, analog, or arbitrary driving signals. It also depends on the behavior of the load component in an interconnect, which itself can behave as a capacitive circuit, inductive circuit, or resistive circuit. This can be summarized by looking at the impedance spectra of the source, trace, and load in an interconnect.

Just like the impedance spectrum for a trace can exhibit very close to inductive circuit behavior at low frequencies, real components can behave like inductive circuits at a range of frequencies. Real components can behave as a purely resistive, capacitive, or inductive circuit in different frequency ranges. When adding any component to a real interconnect, you’ll need to measure its impedance spectrum to determine if it really is an inductive circuit.

If you are working in an application where signal integrity is a major concern, your best bet is to measure the impedance spectrum of an inductive circuit with a vector network analyzer. This will normally return the S-parameters (make sure you de-embed the S-parameters for the connectors!). You can then calculate the impedance from your measurements at each frequency. You will then need to use this information for impedance matching in a real circuit. Vector network analyzer

## Bringing it Together: Inductive Circuits in Real Interconnects

In a real interconnect, the impedance spectra of the trace and the load component will determine whether the trace impedance and component impedance are matched at specific frequencies. With analog frequencies, you only need to worry about matching the impedance of the load component to the trace impedance at one specific frequency. This is trivial in an inductive load that will be used at a single frequency; you only need to design an impedance matching network that sets the load impedance to a specific value at the frequency of interest.

With modulated signals or if you are intending to work with a range of analog signals, impedance matching with an inductive load becomes more complicated as you need to ensure that the matched impedance spectrum of the load component is flat throughout the signal’s bandwidth. Analog components like amplifiers should not behave like an inductive circuit and should have a flat impedance spectrum (i.e., resistive) throughout their bandwidth. Your goal should be to design an impedance matching network that makes the load’s impedance spectrum appear flat (i.e., resistive) in the relevant frequency band. One option is to design an RC circuit between the load’s input and ground as this will help to compensate the inductive behavior of the load component.

With a digital signal, impedance matching at every harmonic becomes more difficult with an inductive load compared to a capacitive or resistive load. A load that behaves as an inductive circuit still needs to be compensated so that the impedance spectrum throughout the load’s bandwidth is flat, it’s just that the bandwidth of a digital signal can be extremely large. With a resistive load, this isn’t a problem; the load impedance is the same at all frequencies, and you can just use a resistor for impedance matching. With a capacitive or inductive load, you now need to design an impedance matching network so that the load’s impedance spectrum is as flat as possible throughout the digital signal’s power spectrum. Plotting impedances on a Smith chart is one way to graphically match impedance over a range of frequencies.

Approximately 75% of the power spectral density in a digital signal is concentrated between the clock frequency and the knee frequency (approximately 0.35 divided by the signal rise time). With a low frequency clock that switches much faster than TTL speeds (i.e., ECL), you could have a difficult time creating a flat impedance spectrum with an inductive circuit as the signal bandwidth can reach several GHz. Using simulation tools for designing impedance matching networks can greatly help in this area.

The right PCB layout and design software can help you create interconnects and circuits with desired resistive, capacitive, inductive, or more complicated behavior. Allegro PCB Designer and Cadence’s full suite of design tools are built to help you design and analyze your layout, and determine when a subcircuit in your board will behave as an inductive circuit. This helps you ensure signal integrity in high speed and high frequency designs.