S-Parameter Simulation Noise Analysis

During an S-parameter simulation, you can calculate these noise characteristics:

• Noise figure
• Noisy 2-port parameters

Each are discussed in the sections that follow.

For networks with more than two ports, the noise figure can be measured between two user-specified ports using Input Port and Output Port; the other ports are treated as resistors for the noise simulation.

Hint To aid in noise figure measurements, use the noise circle measurement component, NsCircle or the function ns_circle. See ns circle().

Noise Figure

The parameter nf(k) in the dataset is the noise figure at output port k. You can view results using the Data Display. The noise figure for each port will appear in the variables list as nf(1), nf(2), and so on. nf displays noise figures for all ports.

When noise figure is calculated at a port, the other ports in the network are terminated in their respective impedances.

For a 2-port circuit, the noise figure is the signal-to-noise ratio at the input, divided by the signal-to-noise ratio at the output. It has units of dB. For a circuit with more than two ports, the noise figure is the ratio of the total noise at the output port to the transmitted input noise. The total noise is the transmitted input noise plus the noise contributed by the network. The transmitted input noise represents the portion of the incident thermal noise (kTB, where k=Boltzmann's constant, 1.380658 x 10 ^-23 J/K, T=290 K, B=1 Hz) which passes through the system.

Calculating Noise Figure

The common definition of noise factor is signal to noise at the input divided by the signal to noise at the output or

This definition describes the way that noise is computed in Advanced Design System.

The noise of the network without the ports is computed and denoted by

For more information on how the network noise is calculated, see Linear Noise Simulation Description.

The port noise is computed separately, and the noise figure equation is written as:

If there are multiple ports, the noise figure at output port k is generalized as:

Note that the output port noise is never included in the summation of noise sources. This definition makes it possible to generalize the noise figure calculation to the case of n-port networks, and in the limiting case of N=2, the calculation agrees with the classic 2-port definition.

For a circuit with more than two ports, the noise figure to all ports is calculated by default. For large circuits with many ports, this can be slow, especially when there is typically only one noise figure that is needed or meaningful. If the noise input port and noise output port are identified in the S-parameter simulation setup, only the one noise figure from the input port to the output port will be computed. In addition, the noisy two-port parameters (NF _min, R _N, and S _opt) will be computed for these two ports. If either or both of the noise input port and noise output port are not specified, all of the noise figures will be calculated.

Noisy 2-Port Parameters

NF _min, R _n and S _opt are the noisy two-port parameters. They describe the noise properties of a two-port and how the noise changes with respect to the source impedance. They describe circles of constant noise figure on the Smith chart.

NF _min is the minimum noise figure that the circuit can produce, when the source has the optimum reflection coefficient S _opt.

R _n is the noise resistance and controls how fast the noise increases as the source reflection coefficient changes from S _opt.

where

, and is the reflection coefficient of the source.

Reference: G Gonzalez, Microwave Transistor Amplifiers, Prentice-Hall, 1984, p 142.