# A/RF Circuit Analysis: Simulation Across Frequency Spectrums

July 5, 2019

Have you ever wished that you could predict the future?  ….of anything? Sure, we’ve seen plenty of movies and books that talk about going back and forth in time. Historical accounts depict individuals—or seers—who would go into a trance-like state and begin uttering or writing about future events.  Nostradamus anyone?

In electronics, we can use dynamic analysis to predict the behavior of circuits. In this instance, we want to connect theoretical results obtained from analysis and equations with actual measures that, in turn, connect us to practical results.

## Kenneth, What is the Frequency?

Before we slip our seer hats on, let’s talk about circuits. Yes, I know, that’s quite a switch. But, when we progress to the end of this article, the switch may seem well… predictable.

Radio frequency (RF) refers to a range of frequencies for signals transmitted and received in a system. The frequency range for RF signals spans from 900 MHz to 2.4 gigahertz. Within an RF transceiver, the RF stage takes weak signals within the frequency band received at the antenna and boosts the signals to usable levels.

Starting with the antenna, the performance of the circuit relies on bandpass filters at the antenna to reject any out-of-band noise. At this point, the signal remains very small and stays within the microwatt range. A pre-amplifier or low-noise amplifier (LNA) provides the gain needed for the signal to become usable at the receiver.

Frequency can range across spectrums, ensure your signal operates accordingly

The RF circuit extracts information from the RF signal by converting the signal to the baseband frequency range. Retrieving the signal in the frequency range that works at the receiver requires the down conversion of the very high GHz signal to a signal in the kHz range. Mixing the RF signal with a large local oscillator signal allows the circuit to down convert to a fixed intermediate signal. At the lower frequencies, active components perform noise and image rejection. Varying the frequency of the local oscillator signal allows the circuit to down convert channels at a different frequency band to the same intermediate frequency.

## Let’s Make Some Noise

Designing PCBs that include RF signals can become challenging because of noise—or any desired signal that corrupts the desired signal. With very small input signals arriving at the receiver, noise can limit sensitivity. Indeed, the key specifications for the RF stage are sensitivity and noise figure. Sensitivity indicates the smallest signal that the RF stage can accept while still providing a usable signal output with a satisfactory signal-to-noise ratio (SNR).

To further complicate matters, amplifiers in an RF circuit can generate noise signals at frequencies similar to the received RF signal. In addition, digital circuits adjacent to an RF transceiver also generate noise that can couple through power supply lines and the PCB substrate. Switching digital signals to the circuit nodes than downgrade the overall signal-to-noise ratio.

Within a PCB design, we can minimize noise with separate power supplies and grounds for the digital and RF portions of a system. Mixing the RF and digital parts of the design allows noise propagation. Your design should also separate the RF stages such as the oscillator and amplifiers. Next, we can use larger bypass capacitors to remove unwanted high frequency signals on the supply network, and minimizing the trace lengths. Before applying these and other solutions, we need to predict noise performance at the individual component level and at the system level.

## Time-Domain, Frequency-Domain Analysis, and the Fourier Transform

A time-domain analysis illustrates how a signal changes over time. Voltage and current measurements occur with respect to time. As time progresses, the signal can vary. During our quick tour of RF circuits, though, we found discovered lots and lots of frequencies and changes in frequency.  So, we need to use something different than time-domain analysis.

Instead, we use frequency-domain analysis to predict noise performance in an RF circuit. Frequency domain analysis describes the signal in terms of its frequency components. Because the frequency domain representation plots the spectrum or all the phase and magnitude components of each frequency, the analysis includes information about the phase shift applied to each frequency component. Having this information allows us to recover the time signal with a combination of individual frequency components.

We can use several different methods to gather frequency domain information from the time domain representation for PCB design.  You could:

• Rely on a theoretical ideal and perform the mathematical integration of the frequency over time

• Use mathematical operators called transforms to convert a signal between the function of time (x(t) to a function of frequency X(ɯ).  The Fast Fourier Transform (FFT) uses calculations or algorithms to convert a function into the sum of an infinite number of sine wave frequency components

• Perform a spectral analysis

• Use simulation software

Because solving the time/frequency problem with the first solution requires knowing the mathematical integrals of many functions and may take an infinite number of reams of paper, we’ll focus on the last two solutions.

The Fast Fourier Transform precisely describes the signal according to its frequency content.  All this occurs by taking the complex signal variations and translating everything into frequency-domain components. Any signal consists of the sum of individual sine waves of the correct frequency, phase, and amplitude. Having this description gives us a frequency-domain picture of the correct signal.

In addition to providing a picture of the correct signal, the description also shows any differences between signals that seem similar. Although two signals may have the same oscillation at the fundamental frequency, each signal may produce different, additional oscillations at integral multiples of the fundamental or different harmonics. The frequency spectrum shows the difference in harmonics or harmonic distortion.

Radio frequencies can be among the tougher signals to design for

If we had the actual circuit in front of us, we could apply the actual signal to the input of a spectrum analyzer and see the frequency spectrum. Spectral analysis collects data over a specific number of cycles and then averages the frequency content of the cycles to produce a spectral shape. As a result, we can use spectral analysis to see harmonic distortion and noise.

When we work with PCB design software, however, we work with simulations rather than the actual physical circuit. Before we can move the design to production, we select the number of layers, components, and layout that give the performance that we seek.

Simulations establish the best method for effectively testing the behavior of the board and components under signal conditions. For example, you can use PSpice transient and Fourier analyses to evaluate circuit performance in response to time-varying sources. You can also use the PSpice Performance Analysis tools to compare the characteristics of a family of waveforms and the PSpice AC sweep analysis to show how voltages and currents in a circuit change with frequency.

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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