Dear Agilent,

I read carefully your Application Note 150-2 and because for the first sight some parts of it was not clear I started to evaluate some equations to find the voltage law for desensitization factor and so on. Now I have some equations and everything seems to be good because they give me nearly the same results (difference is about 1dB or less) as the measurements (I use Agilent EXA N9010A) when I measure a pulse train. No ISI and the spectrum is also ok, so the RBW is set properly

I understand the pulse desensitization factor and its voltage law, the peak power measurements are also ok. But I had some problems with the average measurement and I would like to clear some things.

I found in the menu of the SA that I can set the averaging as voltage average or power average (RMS) or log power. I have the equations for the first and he second method but I would like to check if I am right with the following assumptions regarding to the operation of the SA.

I set the SA the lin scale instead of log because I used linear model for my equation. I checked the spectrum and after I set zero span to see the pulse train (actually the response of the IF filter, no video filter applied). V_{peak}=27mV, f_{carrier}=10MHz T_{eff}=12.9us, T_{bin}=2.73ms, PRF=1/T_{bin}, RBW=3.3 kHz, VBW=1 MHz. I took into account the filter type of IF filter and its bandwidth definition (gaussian 3 dB bandwidth) in my equations. I measured -67,9 avg power and the calculation gives the same result. If I set half of the T_{eff} the power drops 6 dB. The situation is the same if I double the T_{bin}. So they follow the voltage rule and the RBW has no effect until I keep the rules (RBW<0.1/T_{eff}, etc.). It confirms my equation P_{voltage avg}=V^2_{peak}/2/Z_0*(T_{eff}/T_{bin})^2. I suppose that the SA first average the envelope of the voltage (peak detector) then square it and divide it by 2 (to get RMS) and by Z_0 to get power. When I measured the average I set video BW to 1 Hz.

Am I right?

In case of average power (RMS) mode I suppose the SA square the voltage and average it, divide it by 2 and by Z_0. Am I right? For this case I have P_{power ang}= V^2_{peak}/2/Z_0*(RBW)*T^2_{eff}/T_{bin}. Power law for RBW and 1/T_{bin} and voltage law for T_{eff}. The measurement results and calculations are the same and confirm the equations. When I measured the average I set video BW to 1 Hz.

Your notes on page 8 says P_{avg}=P_{peak}*T_{eff}/T_{bin}. That is something else that I cannot understand.

Tom

I read carefully your Application Note 150-2 and because for the first sight some parts of it was not clear I started to evaluate some equations to find the voltage law for desensitization factor and so on. Now I have some equations and everything seems to be good because they give me nearly the same results (difference is about 1dB or less) as the measurements (I use Agilent EXA N9010A) when I measure a pulse train. No ISI and the spectrum is also ok, so the RBW is set properly

I understand the pulse desensitization factor and its voltage law, the peak power measurements are also ok. But I had some problems with the average measurement and I would like to clear some things.

I found in the menu of the SA that I can set the averaging as voltage average or power average (RMS) or log power. I have the equations for the first and he second method but I would like to check if I am right with the following assumptions regarding to the operation of the SA.

I set the SA the lin scale instead of log because I used linear model for my equation. I checked the spectrum and after I set zero span to see the pulse train (actually the response of the IF filter, no video filter applied). V_{peak}=27mV, f_{carrier}=10MHz T_{eff}=12.9us, T_{bin}=2.73ms, PRF=1/T_{bin}, RBW=3.3 kHz, VBW=1 MHz. I took into account the filter type of IF filter and its bandwidth definition (gaussian 3 dB bandwidth) in my equations. I measured -67,9 avg power and the calculation gives the same result. If I set half of the T_{eff} the power drops 6 dB. The situation is the same if I double the T_{bin}. So they follow the voltage rule and the RBW has no effect until I keep the rules (RBW<0.1/T_{eff}, etc.). It confirms my equation P_{voltage avg}=V^2_{peak}/2/Z_0*(T_{eff}/T_{bin})^2. I suppose that the SA first average the envelope of the voltage (peak detector) then square it and divide it by 2 (to get RMS) and by Z_0 to get power. When I measured the average I set video BW to 1 Hz.

Am I right?

In case of average power (RMS) mode I suppose the SA square the voltage and average it, divide it by 2 and by Z_0. Am I right? For this case I have P_{power ang}= V^2_{peak}/2/Z_0*(RBW)*T^2_{eff}/T_{bin}. Power law for RBW and 1/T_{bin} and voltage law for T_{eff}. The measurement results and calculations are the same and confirm the equations. When I measured the average I set video BW to 1 Hz.

Your notes on page 8 says P_{avg}=P_{peak}*T_{eff}/T_{bin}. That is something else that I cannot understand.

Tom

First of all, I am assuming you are using trace averaging; please let us know if you are not using trace averaging. When you use trace averaging, you are averaging each sweep point from one sweep with the corresponding sweep point in subsequent sweeps. You are not performing an average over several sweep points. For more insight into how trace averaging works, refer to Application Note AN-150 (http://cp.literature.agilent.com/litweb ... 2-0292.pdf)

Therefore, to make a measurement as you have described, it is important that each sweep point represent a time-duration of one period, in this case 2.73 ms. I assume that is what you meant by your term T_{bin}. This means that if you have Sweep Points (set under the Sweep/Control menu) set to 1001 (the default value for the N9010A), you would be using a sweep time of 2.73 seconds ( (1001-1) x T_{bin}).

When making pulse measurements in zero span, it is best to set the RBW much greater than the modulation rate (in this case, much greater than the pulse width). In the examples in AN-150-2, you will notice that the zero span measurements uses a 100 kHz RBW when 1/T_{eff} = 10 kHz. You have a T_{eff} of 12.9 us, which say that the RBW should be much greater than 77.5 kHz. An RBW of 1 MHz or wider would be fine.

When the Averaging Type is set to Voltage Avg, the filtering and averaging processes work on the voltage of the envelope of the signal as you described. Once the averaging has been performed, it is converted back to whatever units the user has selected as the Y-axis unit for display.

When the Averaging Type is set to Power (RMS), the filtering and averaging processes work on the power (or square of the magnitude) of the signal, instead of its log or envelope voltage. Again, once the averaging has been performed, it is converted back to whatever units the user has selected as the Y-axis unit for display.

The average power of a pulse is simply the peak pulse power multiplied by the duty cycle. This represents the average power supplied by the transmitter during one pulse period. If the duty cycle is 10% (for example a pulse width of 1 ms and a pulse period of 10 ms) the peak pulse power is only present for 1ms, but that power gets averaged out over a 10 ms period. Therefore the average power is equal to 10% of the peak pulse power.

If we use the parameters of your pulse train, this means that Pavg would be 23.26 dB below the peak pulse power, Ppk (-23.26 = 10 log (T_{eff}/ T_{bin}) ). Since the peak pulse power is -18.36 dBm, the P_avg would be -41.62 dBm.

Regards -