# RLC Circuit Analysis in Your Schematics and Layout

December 4, 2020

### Key Takeaways

• RLC circuit analysis forms the language used to build and understand circuit models for linear time-invariant (LTI) systems with reactive impedance.

• Building a circuit model for a complex electrical system takes some experience and foresight, where real circuit elements and parasitics are combined to form an equivalent RLC network.

• Once you have an RLC model for your system, you can use some basic RLC circuit analysis techniques to simulate electrical behavior.

Resistors, capacitors, and inductors form an RLC circuit.

RLC circuits aren’t just fundamental circuits from electronics classes, they also provide a language to explain the behavior of any linear electrical system with reactive impedance. All RLC circuits can be built from an arrangement of resistors, capacitors, and inductors, which can be used to model electrical behavior in a linear time-invariant (LTI) system. The system you might want to model may not have any real capacitors or inductors in it, but it may exhibit capacitive or inductive impedance regardless.

When you need to analyze a real RLC circuit, or a model for a more complex electrical system like a set of transmission lines, you can use the same set of analysis tools as long as you can build an RLC model for your system. The RLC model you use gives you a simple way to examine things like impulse responses, cascading, and transfer functions in your circuit model. Here’s how RLC models are created and what you can examine in your circuit models with the right set of analysis tools.

## From PCB Layout to RLC Circuit Models

Building a circuit model for a complex electrical system takes some experience and foresight, where real circuit elements and parasitics are combined to form an equivalent RLC network. A real LTI system can be modeled as an RLC network because resistors, capacitors, and inductors are the fundamental circuit elements that describe how voltage and charge in a circuit interact with the electric and magnetic fields.

An RLC model for a system is not complete until it contains both the real circuit elements and parasitics. When taken together, parasitics will create some deviation from the ideal electrical behavior in your designed RLC network. Part of RLC circuit analysis is to examine the contribution of these two points together to better understand the electrical behavior of a real PCB layout.

### Parasitics in a PCB Layout

As much as we’d like a schematic to be a perfect representation of real circuits in a PCB layout, this simply isn’t the case. Parasitics arise as unintentional R, L, and C elements between your intended circuit elements. These elements combine and add to the total impedance of a circuit, sometimes in complex ways. You can spot different parasitic elements in a PCB layout in the following areas:

• Parallel conductors: Anytime two conductors are arranged in parallel, they will have some parasitic capacitance. When there is some non-zero potential between the conductors,  a displacement current will flow between them, adding to the total current in the circuit.

• Current loops: Any loop of conductor, including planes and a conductors bridge with some impedance, will have some parasitic inductance. Any alternating magnetic field can then induce a current in the conductor loop; this is arguably one of the most common causes of low EMI immunity

• DC Resistance: Any conductor that carries a current will also have some DC resistance, which will add to the total impedance of the system.

Obviously, the environment in a PCB layout adds some R, L, and C elements to the actual circuits in your schematics, and the resulting circuit behavior can be quite complicated. Physically, these parasitics account for things like transmission line impedance, pad capacitance, via inductance, and other well-known effects in a real PCB layout. Once you’ve determined where parasitics can be found in your PCB layout and where they should sit in your RLC circuit model, you can run simulations from your schematics to examine electrical behavior.

## What to Simulate in RLC Circuit Analysis

SPICE simulations form the basis for RLC circuit analysis, both for extracting the values of parasitic elements and examining electrical behavior. There are some basic simulations that should be performed as part of RLC circuit analysis:

• Transient analysis: Real systems in a PCB are driven with a range of inputs; these are not just DC or harmonic AC sources. Simulating a circuit response in the time domain is a central part of RLC circuit analysis. The goal here is to visually determine phase delay through the system, gain/loss, and overall signal distortion due to the system’s reactive impedance.

• Transfer function: The transfer function shows the AC frequency response in an RLC circuit model and can be used to determine the output from a circuit at a specific frequency. A related simulation is pole-zero analysis, which returns resonant frequencies and damping constants in a single simulation.

• Parametric sweeps: This simulation is all about extracting parasitics and optimizing a design. By iterating through a range of values, you can see how important signal metrics (e.g., voltage or current, signal distortion, phase delay, etc.) are affected by the value of a parasitic or circuit element. Take a look at this article to see how you can extract parasitics using parameter sweeps.

Whether you’re analyzing a circuit before layout, or you’ve determined parasitics post-layout, you can use these core simulations to better understand your RLC circuits.

Results from a typical frequency sweep simulation in a circuit with multiple RLC networks is shown below. For a single RLC network, you might be easily able to calculate the circuit’s resonant frequency but this is not so easy in a real RLC network where parasitics may be present. Here, we can easily see the intended resonant frequency in the network (~505 MHz), plus an additional unintended high-Q resonance in the network with some complicated bandpass behavior at low frequencies.

RLC circuit analysis frequency sweep results can be used for further circuit optimization.

If your circuit is part of a high speed or high frequency electrical system, you’ll often need to extract the S-parameters for your RLC network. Once you have the S-parameters, you can convert them into ABCD parameters, which makes it easy to see how your circuit model fits into a cascaded circuit network. Using ABCD parameters is by far the easiest way to examine impulse responses and high frequency responses in high speed and high frequency circuits.

Once you’ve designed your schematics and performed RLC circuit analysis, you can use the best PCB layout and design software to capture your designs as an initial PCB layout and begin arranging components. Allegro PCB Editor includes the features you need to layout boards for any application, as well as advanced routing and design verification tools. You can then use Cadence’s analysis tools to simulate and analyze the behavior of your high speed and high frequency electronics.

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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