# Cascade Analysis

Click here to go to our page on noise figure (includes a gain/NF cascade example)

Click here to go to our calculator page to check out our three-stage cascade calculator

**Updated December 2022: ** Due to lack of demand and the pain associated with collecting small money from cheap microwave engineers, we stopped trying to sell the Cascade Analysis Excel workbook way back in 2006. Then we said, if you ask nicely, maybe we'll give you the full version for free. Which sounded fine at first, but lately we've been getting so many requests that we keep falling behind in fulfilling them. If you asked nicely (or just thought about doing so) and we didn't respond, our apologies. Go ahead and grab the full workbook over on our download page!

Here's a clickable outline for this page:

### What is cascade analysis?

Cascade analysis is a simple yet powerful tool for analyzing system performance. You can analyze small-signal gain and noise figure nearly exactly, and come pretty close to modeling large-signal performance, such as predicting one-dB compression point.

Everyone and their little brother has created an Excel spreadsheet for performing Cascade analysis. The noise figure equation is fairly simple. Adding a decent nonlinear equation for large-signal performance is a lot more complicated. But here at Microwaves101, we have already done that and much more for you in a convenient analysis tool!

### Small-signal analysis

Under ideal small signal conditions, gains and losses of cascaded components merely add up in decibels. However, in real life you will have have the added effects of mismatch losses and sneak paths. Cascade analysis doe nothing to address these errors. Be sure to chose components that are well matched in impedance and you won't have to worry about this.

### Noise figure analysis

Noise figure of a cascade follows the well-known Friis equations:

You can learn more on our noise figure page, which goes through the math on an example receiver. Meet Harald Friis in our Microwave Hall of Fame!

### Large-signal analysis

Large signal analysis that can be done in a simple spreadsheet includes compression point and saturated power calculations.

The graph below illustrates three input/output power response curves. The "linear" curve simply assumes that the output power in dB will be higher than the input signal by a constant (the gain, 18 dB in the plot). In the "cubic" relationship, the compression characteristic has been fit from small-signal up to saturation with a cubic polynomial. This works great, until you over-saturate your component and the calculated gain starts to decrease. In real life the output power will most likely saturate for all further increases in power. We call this the "saturated cubic" model. This is what we use in our cascade analysis tool. Note that this type of curve should not be applied to square-law devices such as frequency doublers and detectors.

The Unknown Editor burned some midnight oil and prepared the best known cascade analysis tool ever, so you will never have to. We call it Cascade101.xls. It has ALL of the following features:

- Predict gain, noise figure, P1dB, Psat.
- Predict Pout for any Pin (each stage and entire chain).
- Small file size, many copies fit on one floppy.
- Printer and eyesight-friendly sheets!
- All computational cells are annoyingly locked!
- Analysis of 30 stages! )
- Simultaneous and independent analysis of two input signals (signal plus jammer).
- Analysis of thermal noise as it moves through the chain (noise power and signal/noise ratio are calculated).
- Optional tolerance analysis of all gain, noise figure and P1dB for each stage.
- Optional temperature coefficients for gain, noise figure and P1dB for each stage.
Click here to go to our download area and grab the FREE Cascade101 Analysis Worksheet.

**Author : **Unknown Editor