Verilog-A Noise Modeling

Introduction¶

Noise modeling plays a crucial role in the simulation and analysis of analog and mixed-signal circuits. As technology advances into deep-submicron regions and higher-frequency operation becomes mainstream, accurate prediction of noise becomes critical to ensure system performance and product reliability. Verilog-A provides powerful built-in constructs for representing noise in compact models, components, and behavioral circuit blocks.

Noise affects nearly all aspects of analog and RF design, including:

• Signal-to-Noise Ratio (SNR)
• Bit-Error Rate (BER)
• Phase noise in oscillators and PLLs
• Gain and linearity in RF amplifiers
• Resolution of ADCs and DACs
• Sensor sensitivity and stability

Accurate noise modeling allows early design optimization and prevents silicon failures that arise from noise-dominated circuits.

Fundamental Noise Types¶

Noise originates from physical processes within semiconductor devices. The most significant types include:

Verilog-A supports behavioral modeling of all of these phenomena.

Noise Modeling in Verilog-A¶

Verilog-A enables noise contributions using built-in functions. These functions do not affect DC operating point but appear in:

• Noise analysis
• AC analysis
• Transient noise simulations (if enabled)

Built-in Noise Generators¶

The "label" must be unique per noise source for correct attribution in analysis reports.

Adding Noise to Device Models¶

Noise must be associated with a physical current or voltage contribution.

Example — Diode Noise¶

I(d,a) <+ Is * (limexp(V(d,a)/Vt) - 1);
I(d,a) <+ white_noise(2*`P_Q*abs(I(d,a)), "shot_noise");

White noise here corresponds to shot noise in diodes and BJTs:

$$i_n^2 = 2qI$$

Example — Flicker Noise¶

I(d,a) <+ flicker_noise(Kf*abs(I(d,a))**Af, 1.0, "flicker");

Parameters:

• Kf — flicker noise coefficient
• Af — bias exponent

Compact MOSFET Noise Example¶

Advanced models (BSIM, PSP, HiSIM) combine multiple noise mechanisms:

I(d,s) <+ white_noise(gamma*4*`P_K*$temperature*gm, "channel_noise");
I(g,s) <+ white_noise(delta*4*`P_K*$temperature*gds, "gate_noise");
I(d,s) <+ flicker_noise(Kf*(gm**2), 1.0, "flicker_noise");

Captures:

• Channel thermal noise
• Gate-induced noise
• 1/f behavior

Noise in Passive Components¶

Thermal noise in resistors is given by:

`include "constants.vams"
I(p, n) <+ white_noise(4*`P_K*$temperature/R, "R_thermal");

Which models Johnson-Nyquist noise:

$$\overline{i_n^2} = \frac{4kT}{R}$$

Transient Noise Simulation¶

Some simulators allow time-domain random noise enabling:

• Eye-diagrams
• BER prediction
• Clock jitter
• Oscillator phase noise approximation

Example noise injection:

V(out) <+ white_noise(N0, "transient_noise");

Transient noise simulations must be explicitly enabled in most tools.

Table-Driven Noise Modeling¶

When lab characterizations are available:

NoisePSD = noise_table(freq_vector, noise_vector);
I(out) <+ NoisePSD;

Useful in:

• RF front-ends
• MEMS microphones
• CMOS sensors

Tips for Simulation Stability¶

Best practices:

• Keep noise sources physically meaningful
• Use limiting functions like limexp()
• Validate across DC → AC → Noise → Transient
• Ensure charge conservation

Complete Example: Noisy Resistor¶

`include "constants.vams"
`include "disciplines.vams"

module noisy_resistor(p, n);
    inout p, n;
    electrical p, n;
    parameter real R = 1k from (0:inf);

    analog begin
        V(p,n) <+ R * I(p,n);
        I(p,n) <+ white_noise(4*`P_K*$temperature/R, "thermal_noise");
    end
endmodule

This model fully supports:

• DC
• AC
• Noise
• Transient (if enabled)

Looking Ahead: Modern Noise Challenges¶

Noise modeling is increasingly critical as circuits approach physical and thermal limits.