*Do you know how this inductor will affect the impedance of a circuit?*

We all learn in basic electronics classes that every circuit element has some resistance, but equally important is the impedance of your circuits. In real circuit boards, which generally operate with switching digital signals or oscillating analog signals, impedance affects how signals propagate through the board, how power is transferred between components, and how signals bleed into unwanted areas of your PCB.

There are a number of analyses you can use to determine the impedance of a circuit, but these do not always produce realist results unless you include the right parasitic elements in your models. If you are testing a prototype or designing a circuit for use with high speed or high frequency signals, you’ll need to have an understanding of the parasitic elements that affect the impedance of a circuit.

It is also important to understand how the impedance of a nonlinear circuit is affected by the input signal level, as the impedance of a nonlinear circuit element is really a function of the input. Analyzing the impedance of a circuit with nonlinear components becomes more complicated and requires a different class of analysis techniques.

## What Determines the Impedance of a Circuit?

At the most basic level, the impedance of your circuit depends on the arrangement of your components. Resistors, inductors, and capacitors are the three fundamental linear circuit elements. Resistors can be classified as components that only provide resistance to DC signals, i.e., the relationship between voltage and current does not depend on the frequency of the input signal. In contrast, capacitors and inductors provide reactance, which is a purely complex quantity that is some function of frequency. Ideal capacitors have reactance that is inversely proportional to the signal’s angular frequency, and ideal inductors have reactance that is directly proportional to the signal’s angular frequency. The impedance of a circuit is the sum of resistance and complex reactance.

At a deeper level, your traces have some impedance as they cannot be considered as long inductors. The board itself will affect the impedance of a circuit and your traces. The insulating PCB substrate creates parasitic capacitance, while the arrangement of traces and planes in interior layers creates parasitic capacitance and inductance. These parasitic effects contribute to capacitive crosstalk, and they determine the impedance of transmission lines and your power delivery network.

## Impedance of a Circuit with Linear and Nonlinear Circuit Elements

Linear elements are the simplest circuit elements in that their impedance is not a function of the input voltage. This means that the output current and/or voltage can be easily calculated using the standard rules in circuit analysis for DC and AC circuits. The Gauss-Jordan method used in SPICE-simulators is defined in terms of impedances of linear and allows you to examine the equivalent impedance of a circuit in terms of the impedance of each circuit element. In the time domain, the arrangement of circuit elements will affect the transition to steady state behavior, which can be analyzed with transient analysis or pole-zero analysis.

In contrast, nonlinear circuits contain elements like diodes, transistors, amplifiers, and other elements where the output is a nonlinear function of the input signal strength. The impedance is actually defined in terms of the transimpedance at a particular input signal strength. In other words, if the input signal strength changes, so will the transimpedance of each nonlinear circuit element, as well as the equivalent impedance of the circuit.

Understand nonlinear and linear contributions to impedance is very important in circuit design and analysis, as well as for interpreting the results from tests with a PCB prototype. Ultimately, your test results should inform potential design changes, where the goal is to ensure the impedance in your system takes on desired values.

*The right analysis tools and component electrical models can help you analyze the impedance and behavior of circuits in this schematic*

## The Relationship Between Your Layout and Impedance of a Circuit

Analyzing the impedance of a circuit requires understanding some basics from electronics theory, such as Ohm’s law and Kirchoff’s laws. For more complex circuits, and circuits with nonlinear elements, more advanced simulation and analysis techniques are required to determine the impedance seen by a digital or analog signal in a circuit.

In a real PCB layout, the impedance seen by signals can be very different from the ideal value you determined from a schematic due to the presence of the substrate and the arrangement of traces on the board. This gives rise to important effects like coupling between transmission lines and crosstalk, which changes the impedance from ideal values. Real circuits can experience power integrity problems, such as ringing when circuits switch at high frequencies. The impedance of your power delivery network will also deviate from the ideal capacitive behavior at higher frequencies, which contributes to potential signal integrity and power integrity problems.

### Transmission Line Impedance

The impedance of transmission lines can be characterized using a number of impedance values. The most important of these is the characteristic impedance, which is simply the impedance of a transmission line on a PCB in total isolation from any other transmission lines. This value is normally defined to be 50 Ohms, although it may take a different value depending on the signalling standard used in your device. As an example, LVDS specifies that the differential impedance of a differential pair should be 85 Ohms.

The other metrics used to describe transmission line impedance depend on the relative arrangement of two transmission lines. Due to the parasitic capacitance provided by the PCB substrate, and the mutual inductance between two nearby transmission lines, a transmission line can be characterized using even and odd mode impedance, which accounts for coupling between two nearby transmission lines and how the two lines are driven (i.e., in common mode or differential mode). As related metrics, common and differential impedance are related to these other values, bringing the total number of impedance values used to describe transmission lines to five.

If you’d like to learn more, read about analyzing transmission line impedance in your PCB.

*These traces may act like transmission lines if they are long enough.*

### Power Delivery Network Impedance

Your power delivery network will exhibit capacitive impedance at lower frequencies and reduces to the resistance of your power bus in series with your load components and ground return path at DC. This impedance is dominated by the physical separation between your power rails, traces, and internal planes in your board. As the driving frequency increases, mutual inductance between circuits in your board will cause the impedance of your power delivery network to increase. Eventually, the impedance of your power delivery network will exhibit many peaks at high frequencies.

Ideally, the impedance of your power delivery network should be flat within the band you want to work in. For digital signals, the relevant bandwidth is all frequencies between the clock rate and the knee frequency (0.35 divided by the signal rise time). If all harmonics that comprise a digital signal see the same frequency, then the transfer function for a return signal in a ground plane will be flat. The same ideas apply to analog signals travelling throughout your board and ground planes.

While the impedance spectrum is important for identifying a bandwidth that has minimum power delivery network impedance, the spatial distribution of impedance in your ground plane is much more important, particularly in mixed-signal devices. Signals will follow the path of least reactance back to the ground return when travelling in the ground plane. Ideally, the path of least reactance in a star, point-to-point, or multipoint topology should lie directly beneath conductors in your board. This will ensure your circuits have minimized loop inductance and will have least susceptibility to EMI.

If you’d like to learn more, read about power integrity in system design.

*Example power delivery network impedance spectrum*

### PCB Substrate Material Selection and Stackup Design

Due to the parasitic effects mentioned earlier, you’ll need to carefully select a substrate material and design your stackup. The dielectric constant of your substrate will affect the geometry required to produce a transmission line with specific impedance and will affect the impedance of your power delivery network. The presence of planes beneath conductors also determines the loop impedance in a circuit, which affects a circuit’s EMI susceptibility.

If you’d like to learn more, read about stackup design and PCB substrate material selection.

### Impedance Matching Networks

Your stackup will affect plenty of other aspects of your board design, such as its thermal resistance and your routing strategy. When combined with the right substrate material, you can reduce the losses seen by signals while maintaining consistent impedance throughout your circuits. Maintaining the impedance of a circuit to a specific value during routing is important for ensuring impedance matching throughout a signal chain. As signals transition to transmission line behavior, you’ll need to ensure your transmission lines, drivers, and receivers have consistent impedance to prevent signal reflections.

If you’d like to learn more, read about designing an impedance matching network.

*You’ll need to determine the impedance of transmission lines and vias in this layout*

### Via Impedance

Just like a PCB substrate will have some parasitics between neighboring conductive elements, so will vias in a multilayer board. Your vias are essentially small inductors with an air-filled or conductive epoxy-filled core. The inductance of a via is on the order of nanohenries and depends primarily on its aspect ratio. Vias also have self capacitance, and groups of vias have some mutual capacitance and mutual inductance. This leads to noise coupling between vias, and causes vias to act as impedance discontinuities when placed on a transmission line. In general, the use of vias is generally kept to a minimum in high speed and high frequency circuits.

If you’d like to learn more, read about vias in your PCB layout.

## Tools for Managing the Impedance of a Circuit

If you ignore parasitics, and if you ignore real circuit models for your layout, which account for equivalent series/parallel inductance, resistance, and capacitance, you can analyze a circuit layout using good-old pen and paper. If you have access to a SPICE-based simulator, you can easily determine the impedance of a linear circuit using an AC frequency sweep, and you can visualize the transfer function for a circuit in a Bode plot. These tools can be used to show you the total impedance of a circuit block in your design, as well as how a circuit block affects the magnitude and phase of an input signal.

*These vias and conductors will affect the impedance seen by signals throughout your board.*

With nonlinear circuits, you’ll need to use more advanced analyses. The most prominent tool for working with nonlinear circuits is to use a DC sweep as this tells you how a DC input voltage propagates an output voltage and current. When working with AC signals or arbitrary oscillating waveforms, you can use small signal analysis to examine how a change around some operating point. This analysis tells you the transimpedance of a circuit around a specific operating voltage in your circuit. A more powerful technique is harmonic balance analysis, which tells you how a sinusoidal signal and its harmonics behave in a nonlinear circuit.

Cadence’s full suite of PCB design and analysis tools are extremely useful for determining the impedance of a circuit for any application. With Allegro PCB editor, you can design your board and immediately import your design data into Cadence’s SI/PI Analysis Integrated Solution for PCB Design. This set of industry-standard simulation and analysis tools give you a complete view of how your circuit responds to different types of signals.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.

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