## Notes on HB9AJG's E4000 sensitivity measurements

In August 2013, a ham operator with the HB9AJG call sign posted a detailed report on measurements done with two rtl-sdr dongles to the SDRSharp Yahoo group. They used laboratory instruments to evaluate many aspects of these cheap software-defined radio receivers. As lab reports go, this one is very detailed and contains all the information necessary for anyone with sufficient equipment to replicate the results. The author certainly deserves praise for being so diligent.

In my previous blog post, I mentioned that my own measurements of the noise figure of a similar rtl-sdr dongle disagree with HB9AJG's report. My Ezcap DVB-T dongle is using the same Elonics E4000 integrated tuner as the Terratec dongle tested by HB9AJG. While this does not necessarily mean that the two devices should perform identically, it did prompt me to look closely at HB9AJG's sensitivity measurements. During that I believe I have found two errors in the report, which I want to discuss in the following.

Remark 1:The dongles have a nominal input impedance of 75 Ohms, whereas my signal generators have output impedances of 50 Ohms. My dBm figures take account of the difference of 1.6dB.

The first odd thing I noticed about the report is this correction for the mismatch between the signal generator's output impedance and the dongle's input impedance. ~~I'm not sure where the 1.6 dB figure comes from.~~

If we assume the source and load impedances above, the mismatch correction should be:

0.18 dB is small enough to be insignificant compared to the other measurement errors and I ignored mismatch loss completely in my noise figure calculations.

I don't actually know the input impedance of my dongle. 75 Ω seems a fair guess as that is the standard for TV receivers. The E4000 datasheet specifies an even lower loss of around 0.14 dB for a 50 Ω source (see *Input Return loss (50R system)* on page 11). Of course, the dongle might have some additional matching network in front of the tuner and I don't currently have the equipment at hand to measure the mismatch loss directly.

It might be that 1.6 dB figure was measured by HB9AJG. If in fact these tuners are so badly matched, then my measurements overestimate the noise figure for a similar amount. For the purpose of comparing my results with HB9ALG's however, I have removed this compensation from their figures.

*Update: My father points out that signal amplitude on a 75 Ω load in a 50 Ω system is in fact 1.6 dB higher than on a 50 Ω load. I was wrongly considering signal power correction. It is in fact the amplitude of the signal entering the receiver that matters, not the power. In that aspect, HB9AJG's correction was accurate. On the other hand, an Agilent application note pointed out by David in a comment to my previous post shows that accounting for mismatch is not that simple.*

10log(Bandwidth) in my measurements is 10log(500) = 27dB

My second problem with the report is connected with the bandwidth of the measurement. To calculate the noise figure from the minimum discernible signal (MDS), measurement bandwidth must be accurately known. Any error in bandwidth directly translates to noise figure error. HB9AJG used the SDR# software and the report says that they used a 500 Hz filter for wireless (CW) telegraphy in their MDS measurements.

I replicated their measurements in SDR# using the same filter settings and it appears to me that the 500 Hz filter is in fact narrower than 500 Hz. I should mention however that I used version 1.0.0.1333 instead of 1.0.0.135 and my version has a *Filter Audio* check box that the report doesn't mention. It seems to affect the final bandwidth somewhat and I left it turned on.

I believe the actual filter bandwidth in my case is around 190 Hz. This estimate is based on the audio spectrum curve shown on the SDR# screenshot above. The curve shows the spectrum of noise shaped by the audio filter. Since noise has a flat spectrum, this curve should be similar to the shape of the filter gain itself.

A trace of the spectrum is shown in linear scale on the graph above. A perfect square filter with 190 Hz bandwidth (lightly shaded area on the graph) has the same gain-bandwidth product as the traced line. In log scale this is equivalent to 22.8 dB.

Finally, if I take both of these corrections and apply them to the MDS measurements for 700 MHz from HB9AJG's report, the noise figure comes out as:

~~This result is reasonably close to my result of 17.0 dB for the twice-power method.~~

*Update: 1.6 dB figure has the wrong sign in the equation above, since it is due to higher signal amplitude, not lower power as I initially thought. To cancel HB9AJG's correction, it should subtracted, giving NF = 13.6 dB.*

Of course, you can argue that this exercise is all about fudging with the data until it fits the theory you want to prove. I think it shows that noise measurements are tricky and there's a lot things you can overlook even if you're careful. The fact that this came out close to my own result just makes me more confident that what I measured has some connection with reality.

Good blog post. Keep it up.