Topband: FW: The WD8DSB mini-flag antenna (LONG!)

[Michael Tope]

Hi Jim,

 From the P3 manual:/
/

    /"The dsPIC further processes the signal for presentation on the
    480x272-pixel color TFT LCD display. The "circuitry" shown inside
    the processor box in the block diagram is actually implemented as
    software routines. The FFT is the fast Fourier transform, which is a
    software version of a hardware spectrum analyzer. It reads the
    incoming signal and calculates the frequency spectrum. Further
    software routines calculate the power of the spectrum, take the
    logarithm, and then scale and offset the result so that it reads
    correctly in dBm on the display."

    /

The raw samples will be in volts, but what gets displayed depends on the 
processing. The FFT spits out a complex number for each bin. If you take 
the magnitude of that complex number and square it, you get a number 
that is proportional to the power in that frequency bin averaged over 
the length of time that the FFT samples (e.g. 4096 samples @ 60 
Megasamples/sec would be a time interval of 4096/60e6 = 68us).

The random Johnson noise voltage you get from a resistor has a two-sided 
Gaussian distribution with zero mean and standard deviation sigma, so 
the random noise voltage does average to 0 volts. The noise power on the 
other hand has a one-sided Gaussian distribution with a variance of 
sigma^2. If you average after conversion to power (this is what is 
typically done in a spectrum analyzer), the random noise won't average 
to 0.0 watts, instead it will converge toward the average noise power 
(i.e. number proportional to sigma^2). This is why the thermal noise 
displayed on a spectrum analyzer doesn't tend toward minus infinity dBm 
when you average it, instead it tends toward sigma^2 as you apply more 
averaging.

When you calculate KTB and convert that to dBm (e.g. -174 dBm for room 
temperature in a 1 Hz bandwidth), you are getting the sigma^2 value. But 
the Gaussian distribution has tails that extend beyond 1 sigma,  that is 
why the displayed noise has jagged peaks before it is averaged. Some of 
the noise power samples taken in the time interval of the FFT are going 
to be less than sigma^2 and some are going to be significantly greater 
than sigma^2, but if you average enough of them (from any given 
frequency bin), you get a number that converges toward sigma^2.

73, Mike W4EF................

On 2/25/2021 7:39 PM, Jim Brown wrote:
> On 2/25/2021 5:16 PM, John Kaufmann via Topband wrote:
>> The P3 averages power, not amplitude, so using longer averaging times 
>> just
>> smooths the display and doesn't reduce random noise.
>
> It has nothing to do with power. Last I looked, the P3 is reading and 
> displaying the instantaneous voltage in the IF, and can be calibrated 
> to voltage at the input.
>
> I've been doing swept measurements of complex quantities for nearly 40 
> years, first at audio frequencies and now at RF. Averaging DOES cause 
> random contents of a bin to approach zero (or the noise floor), making 
> correlated signals stand out. This has long been well understood.
>
> I the principle to measure the dynamic response of broadcast signal 
> processing in a peer-reviewed paper to the Audio Engineering Society 
> in 1986.  The test signal was a swept sine embedded deep in musical 
> program material to the point that it was barely audible to a trained 
> listener, and detected by a synchronized swept narrowband detector. 
> Because the swept excitation and swept detector are synchronized, the 
> measurement produces the complex response of the system, and program 
> material, being non-coherent, averages out.
>
> http://k9yc.com/AESPaper-TDS.pdf
>
> 73, Jim K9YC
> _________________
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