**EMRFD Message Archive 8633**

MessageDateFromSubject8633 2013-05-06 21:24:21 Lawrence Signal to Noise Calculation of a Receiver Cascade For receiver design there are calculations done on a block by block basis for the receiver cascade and these are covered in EMRFD. There are programs that exist both commercially (cost involved) or are no charge downloads, or you can program yourself in a spreadsheet or otherwise, that calculate the normal parameters such as gain, noise figure, 3rd order intercept points, 2nd order intercept points, and spur calculations for frequency converters (mixers). None of the programs, commercial or free, I have come across lately calculate the signal to noise ratio on a block by block basis. Does anyone know of a program that exists today that will do this calculation? Okay, I might be a bit lazy but why reinvent the wheel? In the late 1980s there was a commercial program called SysCAD, offered by Webb Labs, that would do these calculations. Does anybody have a copy?

73 de (9V1MI, WN8P) Larry8719 2013-06-11 10:47:31 Lawrence Signal to Noise Calculation of a Receiver Cascade In the first half of the 1980s I had a mentor that taught me about

receiver cascade calculations. These calculations not only included the

normal parameters of cascaded gain, noise figure, second order intercept

points, and third order intercept points, but also included a signal to

noise ratio calculation on a stage by stage basis. In the late 1980s

there was a professional PC program called SysCAD offered by Webb Labs

that included these calculations. I have not seen a modern program, free

or professional (for cost), that includes these calculations. EMRFD does

not present these calculations and the homebrew receivers such as Markus

Hansen's, VE7CA, HBR2000; Cornell Drentea's, KW7CD, Star-10; or Martein

Bakker's, PA3AKE, H-Mode Mixer Receiver does not show these

calculations.

Parameters needed for the noise level calculations[1] are the equivalent

noise bandwidth of the narrowest filter that the demodulator sees and

the image frequency rejection of the filters in front of frequency

converters (mixers). For these basic SNR calculations we are only

concerned about the thermal or Johnson noise and the SNR we are

concerned with is what the demodulator sees. I believe it was in

"Solid State Radio Engineering" by Krauss, Bostian, and Raab

that they gave a figure of 10 dB to 12 dB for a CW or SSB signal and 40

dB for a snow free color TV signal. In a receiving system the best SNR

is at the antenna terminals and degrades from there as you go from stage

to stage to the input of the demodulator.

An equation used to calculate a receiver parameter called the minimum

discernible (or detectable) signal (MDS) is given by EMRFD Eq 6.12: MDS

(dBm) = -174 (dBm/Hz) + 10log Bn (dB·Hz) + NF (dB). However, a

Mini-Circuits application note[2] adds a forth term as follows: MDS

(dBm) = -174 (dBm/Hz) + 10log Bn (dB·Hz) + NF (dB) + required S/N

(dB).

As an example of SNR calculation in a receiver cascade lets look at

EMRFD Fig 6.64, which consists of three stages: A BPF, an

amplifier/mixer (the NE602) block, and an IF block. The Z Matching

Network is ignored as its gain and noise figure are 0 dB. The parameters

of these three stages are: BPF G=-2 dB, NF=2 dB; Amp/Mixer G=18 dB, NF=5

dB; IF G=?, NF=10 dB.

For calculations we set the signal input level to the MDS level and see

what happens to the SNR.

At the BPF input: Si=-140 dBm, Ni=-147.0 dBm (based on Bn=500 Hz and

To=290 K), and the S/N is 7 dB (a little low but we move on).

At the BPF output: So=-142 dBm, No=-147 dBm (the noise level can't go

below the noise floor!), and the S/N is 5 dB.

At the output of the Amp/Mixer: So=-124 dBm, No=-121 dBm, and the S/N is

-3 dB. This says the signal level is 3 dB less than the noise level and

would be undetectable. You will have to increase the signal input level

to hear anything.

For calculation of output noise level of a mixer there are two

contributions. One is from the signal frequency and the other is from

the image frequency. The measured output noise power level, considering

the noise contribution from the signal frequency and the image frequency

are equal, is 3 dB higher than it would be from the signal frequency

alone, and thus the NF, if stated, is as if the image frequency noise

was completely rejected. In this case it doesn't matter what the BPF

image frequency rejection is, you can't go below the noise floor.

A calculation of image noise rejection versus degradation in S/N goes as

follows: For 10 dB rejection the S/N degrades by 0.4 dB, for 20 dB

rejection the S/N degrades by 0.04 dB, for 30 dB rejection the S/N

degrades by 0.004 dB, etc. Proof of which is left to the student to do

the calculations and show this is so.

Now let's look at EMRFD Fig 6.65. This adds a BPF and an amplifier ahead

of Fig 6.64. Parameters of BPF1 are: G=-1 dB, NF=1 dB; Amp G=10 dB, NF=3

dB.

At BPF1 input: Si=-142.2 dBm, Ni=-147.0 dBm, and S/N=4.8 dB.

At BPF1 output: So=-143.2 dBm, No=-147.0 dBm, and S/N=3.8 dB.

At Amp output: So=-133.2 dBm, No=-134.0 dBm, and S/N=0.8 dB.

At BPF2 (Fig 6.64 BPF): So=-135.2 dBm, No=-134.0 dBm, and S/N=-1.2 dB.

We haven't even gotten to the Amp/Mixer stage and the signal is already

buried in the noise. The signal level will have to be increased to be

discernible

[1] See "Mohr on Receiver Noise" at

<http://www.ieee.li/pdf/viewgraphs_mohr_noise.pdf> >.

[2] See "UNDERSTANDING NOISE PARAMETER MEASUREMENTS" at

<http://www.minicircuits.com/app/AN60-040.pdf> > Eq 3. Also see

"Understanding Mixers Terms Defined, and Measuring

Performance" at<http://www.minicircuits.com/app/AN00-009.pdf> >.

I offer this information as another tool for design and evaluation of

receivers. Any feedback, discussion, or comments, especially from Wes or

Rick?

73 de (9V1MI, WN8P) Larry

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