Selecting Minimum/Maximum Noise Frequencies for Transient Noise Simulation

Controlling noise is critical when it comes to designing advanced analog and radio-frequency (RF) circuits. In the digital world, designers tend to tackle noise by adding ground planes, shortening high-speed traces, and placing decoupling capacitors close to IC power pins.

However, high-performance analog designs have significantly tighter noise margins. The most important performance metrics in these scenarios — such as signal-to-noise ratio (SNR), bit error rate (BER), phase noise, and timing jitter — rise or fall with noise.

The challenge is that a significant amount of noise is baked directly into the semiconductor devices themselves and, therefore, can’t be avoided. As a result, device noise ultimately sets the fundamental limits of the circuit’s functionality.

The problem is particularly acute in analog circuits with noise-sensitive architectures, including those based on the most advanced CMOS process nodes, where falling supply voltages and rising operating frequencies leave little headroom. The complex building blocks in these designs, including analog-to-digital converters (ADCs), phase-locked loops (PLLs), transmit and receive (Tx/Rx) chains, and high-speed SerDes, all operate close to these limits. Consequently, they’re all susceptible to device noise, which is often highly transient.

Transient noise analysis plays a significant role in analog design by simulating a circuit’s response to random device noise. Unlike a conventional transient circuit simulation, a transient noise simulation models the inherent noise of its circuit elements. More specifically, a transient noise simulation includes thermal noise for non-ideal resistors and MOS/bipolar device noise sources (1/f noise, MOS gate thermal noise, and bipolar shot noise).

When performing a transient noise simulation, values must be specified for the minimum and maximum frequency of the noise sources and simulation accuracy. As outlined in Reference 1, the accuracy of a transient noise simulation is highly dependent on these parameters.

The lowest frequency the simulation can capture is governed by the simulation end time TSTOP. Since a full period of frequency components whose period is greater than TSTOP isn’t included in the simulation data, the magnitude of these frequency components can’t be accurately determined. Thus, a reasonable choice for the minimum frequency of noise sources is 1/TSTOP Hz.

To understand the need for a maximum noise frequency limit in a transient noise simulation, consider the impact of a resistor’s thermal noise on a circuit simulator. Without a limit to the maximum noise frequency, the time increment (i.e., timestep) that must be taken by a circuit simulator approaches zero, as very small timesteps are necessary to include high frequencies of the noise. Therefore, one must set a maximum noise frequency to limit the minimum simulation timestep to a reasonable value.

Oftentimes, it’s not obvious how high the maximum noise frequency should be set for linear and nonlinear circuits. Choosing a large value for the maximum noise frequency forces the simulator to use small timesteps to create the high frequency noise. In turn, it prolongs the simulation time and increases the size of the simulator output file.

Conversely, choosing too low of a value for the maximum noise frequency may not provide an accurate estimate of circuit noise. That’s because any noise components existing above the specified maximum noise frequency will not be included.

Striking the right balance will produce an accurate estimate of noise metrics from the simulation results.

Transient Noise Simulation of Linear vs. Nonlinear Circuits

If the circuit being examined is linear — for instance, an amplifier operating in its linear region — the transient noise frequencies will mirror the noise source frequencies shaped by the gain and bandwidth of the circuit.

There’s no frequency translation of noise frequencies. Consequently, increasing the maximum source noise frequency has no impact on low frequency noise. Thus, an appropriate maximum noise frequency is determined by the bandwidth of the desired noise measurement. If the maximum transient noise bandwidth exceeds the bandwidth of the noise measurement, it will not impact the noise measurement.