RF amplifier IMD Characterization

[fourfathom]

I have a simple RF preamp design I am trying to characterize (see attached).  It uses a single BFU590Q bipolar transistor, which is sort of a replacement for the 2N5109, in a resistor feedback circuit with no inductors.  I'm getting about 20dB of gain, -3dB at 120 MHz.  This is more gain than I need, so I will probably reduce the gain and perhaps in the process improve the linearity.  The V supply is 12V, and the transistor is drawing about 25 mA.

So, measuring the linearity -- At the moment I'm not set up to do good two-tone IMD measurements, so instead I'm looking at 1dB compression (at about -13 dBm output), and I am measuring the 2nd harmonic at various output power levels.  Is there a way, or rule of thumb, to guess at the third-order intercept with just these measurements?  I'm going to eventually build a combiner with good port-port isolation to do actual IMD tests, but would like to have a reasonable quick guess at it.

[Odysseus]

Can you measure the third harmonic?

[fourfathom]

Can you measure the third harmonic?

Easily.  I haven't logged this in my notes, but if that gets me something useful I will.  The 2nd is stronger, because it's a single-transistor class-A amplifier.

[mawyatt]

You can get the 3rd Order Intercept by sweeping the input power and measuring the 3rd harmonic output. Plot these in dBm and they will intersect because the 3rd harmonic scales at 3X. You can get the Input and Output 3rd Order Intercept directly from the plot.

I vaguely remember a relation between 1dB Compression and 3rd Order Intercept for well behaved (no memory) devices, but can't remember details...sorry.

Best,

[fourfathom]

Thanks to both of you!

[G0HZU]

This is a fairly common negative feedback based circuit and I've used it a lot over the years, but not with that particular BJT. Also I've not used the ESD diode at the input.

The old rule of thumb for basic BJT based MMICs from Avantek and Minicircuits (using a darlington arrangement) was that the OIP3 is typically 13-15dB above the P1dB. This applies for relatively small test tones with the output tones about 10dB below P1dB. As you drive closer to P1dB the OIP3 measurement will degrade because the device won't follow the expected slope for the intercept point. From experience, the same rule of thumb can usually be applied to your circuit. However, in your case you have only 0.22R in the emitter. Presumably there will be some stray inductance here too. Having a low resistance here is good for gain but not so good for linearity.

Usually, there will be a resistance of a few ohms here and this will help with linearity at the expense of gain.

I'd expect your current circuit (biased at 25mA) to maybe achieve an output P1dB of about 12dBm and scrape an OIP3 of about +24 to +25dBm. This OIP3 would be slightly less than 15dB above P1dB.

If you introduce some extra negative feedback via some extra emitter resistance you should be able to boost the linearity. I'm not sure the P1dB will improve much, but the OIP3 should get closer to being 15dB above P1dB. It might improve to +28dBm for example.

[Marsupilami]

You can get the 3rd Order Intercept by sweeping the input power and measuring the 3rd harmonic output. Plot these in dBm and they will intersect because the 3rd harmonic scales at 3X. You can get the Input and Output 3rd Order Intercept directly from the plot.

I'm going to be arguing with this, but it's more of a question because I couldn't find anything explicitly stating this and I'm not fully sure in my math.
Using 1st and 3rd order polynomial approximation for the nonlinearity of the voltage transfer function there seems to be a 2/3 (1.76dB) difference in the intercept point derived from a single tone 3rd harmonic, vs derived from the one sided IMD3 of a two tone signal. (That is assuming that the total input power is the same, so both tones in the dual tone case are -3dB compared to the single tone.)
The good thing is that this doesn't depend on the nonlinear characteristic of the device, but something that still have to be taken into consideration as an offset.
Please correct me if I'm wrong, I'd love to see a derivation of this other than mine. Most sources I found muddle the concept of linear power bleeding into different 3rd order products by different ratios.

[mawyatt]

Here's a link that illustrates what we were saying wrt the 3rd harmonic intercept.

This also notes the OP question about the relationship between TOI and 1dB Compression, with the prior ~9.6dB higher.

https://en.wikipedia.org/wiki/Third-order_intercept_point
https://upload.wikimedia.org/wikipedia/en/d/d9/Interceptpoint.png

Best,

[Marsupilami]

Here's a link that illustrates what we were saying wrt the 3rd harmonic intercept.

That's my point, you refer to harmonic intercept, but the plot calls out IM3. The wikipedia article also notes that there are two ways it's defined, based on harmonic or the two tone in-band intermod products. It doesn't explain what is the difference between those two derivations.

There is no exact formula for the relationship between P1dB and the intercept points for similar reasons. It's a simplification.
Just for the fun of it I took the table of ~300 MMIC amplifiers from Minicircuits and here's a histogram of how their specified P1dB differs from the OIP3. The mean and the average is both at 13.5dB.

[fourfathom]

I ended up building a hybrid combiner and ran some two-tone IMD measurements.  The hybrid isolation was pretty bad, but feeding it from two signal generators there wasn't any significant IMD seen on the spectrum analyzer.  The amplifier has a gain of 22.5 dB, and an output 1 dB compression at +8 dBm.  Below is a plot of the output and IMD, with the slopes extrapolated to show a 3rd order output intercept at about +18 dBm.  The gain on this plot looks low because I didn't compensate for the 3.xdB combiner loss.

I also looked at third harmonic levels vs output, and the extrapolated output intercept was about +30dBm (dramatically different than the IMD intercept).

[RFDx]

I have a simple RF preamp design I am trying to characterize (see attached).

The 0.22 Ohm emitter degeneration looks like a typo . With Re=0.22 Ohm the input impedance is ~22 Ohm with the output impedance slightly higher. Re=2.2 Ohm (and even better 2.7 Ohm) leads to an I/O-impedance very close (or equal) to 50 Ohm.

A Spice simulator is very helpful in getting a first clue about the OIP3 of the amp before doing any measurements. With Re=2.7 Ohm and a power gain of Pg=20dB @ IC=20mA, I get a 3rd order output intercept point of OIP3=22dBm with 2 x 0dBm tones (30MHz & 30.5MHz) at the output.

[RoGeorge]

Below is a plot of the output and IMD, with the slopes extrapolated to show a 3rd order output intercept at about +18 dBm.  The gain on this plot looks low because I didn't compensate for the 3.xdB combiner loss.

I also looked at third harmonic levels vs output, and the extrapolated output intercept was about +30dBm (dramatically different than the IMD intercept).

Wikipedia https://en.wikipedia.org/wiki/Third-order_intercept_point says the intersection point should be estimated from measurements at power levels as low as possible:  The intercept point according to its basic definition should be determined by drawing the straight lines with slope 1 and n through the measured data at the smallest possible power level", so just out of curiosity, I've took the pixel coordinates from your 4 measurements, and tested how much the TOI might shift when considering higher power measurements. (because TOI, and 1dB compression, and such, are brand new to me, wanted to get some grasp about them).



Looking only at the lowest power measurements (only the first 2 points), the lines intersect at +30dBm out for a +10dBm in.  That would make intermodulation intercept point at the same value as the 3rd harmonic vs output, at +30dBm out for both.  Is this (+30 in both IMD and 3rd harmonic) just a happy accident because of two fewer point?

[RoGeorge]

looking at 1dB compression (at about -13 dBm output), and I am measuring the 2nd harmonic at various output power levels.  Is there a way, or rule of thumb, to guess at the third-order intercept with just these measurements?

While learning about the topic, bumped into this paper, seems applicable here, too.  It gives a method to calculate third-order intercept from only the gain curve up to 1dB compression, with a single tone:

A Simple Technique for IIP3 prediction from the Gain Compression Curve
Choongeol Cho and William R. Eisenstadt
University of Florida, Dept. of Electrical and Computer Engineering
http://wami.eng.usf.edu/Conferences/WAMICON/2005/Electronic-Materials/posters/tp-1.pdf

[G0HZU]

Just for the fun of it I took the table of ~300 MMIC amplifiers from Minicircuits and here's a histogram of how their specified P1dB differs from the OIP3. The mean and the average is both at 13.5dB.

Thanks. In this case, it's best to only look at the old classic ones from Avantek and Minicircuits as these are simple (darlington) BJT based devices. The old rule of thumb was that the OIP3 is usually 13-15dB above P1dB. It's just a rule of thumb though. The same rule of thumb can usually be applied to small signal class A wideband BJT amps as well.

I've made lots of small signal wideband amplifiers using single BJTs over the years and it is usually possible to estimate the performance of them based on collector current and collector load.
In this case, the load is 310R in parallel with 50R = 43R. This initial simplification ignores the feedback. If 24mA of the 25mA is the collector current then I'd expect to see the top half of the waveform clip at .024 * 43 = 1.03Vpk.  In a 50R load this will be about 10mW or 10dBm. So I'd expect the P1dB to be a bit higher than +10dBm. It will probably be about 11dBm and is unlikely to be higher than about 12dBm. Again, this is just a ballpark estimate based on an old rule of thumb. It's best to build it and test it.

Normally, I'd expect the OIP3 to be about 15dB higher than this but because there is no feedback resistor in the emitter it might degrade a few dB. So that's why I suggested 24dBm as an estimate for the OIP3.

[G0HZU]

I ended up building a hybrid combiner and ran some two-tone IMD measurements.  The hybrid isolation was pretty bad, but feeding it from two signal generators there wasn't any significant IMD seen on the spectrum analyzer.  The amplifier has a gain of 22.5 dB, and an output 1 dB compression at +8 dBm.  Below is a plot of the output and IMD, with the slopes extrapolated to show a 3rd order output intercept at about +18 dBm.  The gain on this plot looks low because I didn't compensate for the 3.xdB combiner loss.

Those results don't make much sense to me (apart from the gain maybe). If the collector current is about 25mA I can't see how the P1dB can be as low as 8dBm. The output intercept needs to be measured at low drive levels as it will deviate from the expected slope at higher drive levels. Your plots show this.

I think the P1dB will be at least 10dBm (probably 11dBm) but it might manage 12dBm. The OIP3 is harder to predict, but I think it will be less than 25dBm and greater than 21dBm.
With a few tweaks to your design you should be able to improve the OIP3 if you include a sensible emitter resistor. It's then possible to adjust the feedback resistors R11 and R8 to optimise the input and output impedance for 50R operation.

[fourfathom]

I ended up building a hybrid combiner and ran some two-tone IMD measurements. [...]

Those results don't make much sense to me (apart from the gain maybe). If the collector current is about 25mA I can't see how the P1dB can be as low as 8dBm. The output intercept needs to be measured at low drive levels as it will deviate from the expected slope at higher drive levels. Your plots show this.

I think the P1dB will be at least 10dBm (probably 11dBm) but it might manage 12dBm. The OIP3 is harder to predict, but I think it will be less than 25dBm and greater than 21dBm.
With a few tweaks to your design you should be able to improve the OIP3 if you include a sensible emitter resistor. It's then possible to adjust the feedback resistors R11 and R8 to optimise the input and output impedance for 50R operation.

I was eyeballing the power and IMD plot points and it looks like I was fooled by the onset of gain compression.  I definitely need to refine my measurement techniques.  That was the first time I've attempted to measure IMD, so I suppose I'm still happy that I could at least get somewhat-usable data.

About the design, (for a start) my emitter resistor is wrong.  It's not a typo, but I was Spicing it and took myself down a rathole in search of gain.  Backing off to more reasonable values, in simulation I can get a 50 Ohm input Z and 19dB gain (using a 2N2222 at 1 MHz since I don't have a model for the actual transistor).  I'm going to change the emitter, feedback, and bias resistors, and make some new measurements.  I will report back.

Thanks everyone for the help!

[RoGeorge]

NXP has a SPICE model for BFU590Q.  Seems to be working in LTspice without changes.  The model has an Imax parameter that is left unused by LTspice, but max currents can be verified manually to stay in the datasheet specs.

Didn't find a SPICE model for ESD8351, so took its advertised 0.55pF and placed that as a capacitor.  Shouldn't matter much if the input signal is small enough.

With the NXP model and LTspice, Zin=50 for R11=2.7\$\Omega\$ (maybe even 2.5, or 2.2, if its effect on Zout is also considered).
Attached zip includes the schematic + the NXP model for BFU590Q.

[G0HZU]

It's also worth deciding what performance parameters are the most important to you. If noise figure is important, then I think the noise figure will degrade if you change the feedback to reduce gain and improve linearity. It's also worth considering stability. With a fast BJT like the BFU590, you would ideally have to analyse or measure it for k factor up to 5GHz or more. This is usually best done with an s-parameter based model of the BJT. However, you don't 'have' to do this analysis if you aren't that concerned about any slight risk of instability. Usually it's possible to improve k by deliberately adding a couple of nH in the emitter connection in series with the emitter resistor. Often the package inductance of the resistor will be enough unless you use a tight SMD layout.

It's probably possible to get a sub 2dB noise figure with that BJT if you don't optimise the design for a 50R input. If you do add some emitter resistance and maybe also adjust R8 to increase feedback, you should be able to improve the OIP3 and the port match but I think the noise figure will begin to creep up. It might head up towards 3dB.
The other way to reduce the noise figure will be to reduce the collector current, but this will obviously affect the linearity. The other option is to add a 4:1 (TLT) transformer at the collector and this will give a big boost in P1dB and OIP3.

[fourfathom]

Thanks again, this has all been extremely helpful.
The application is for a preamp integrated into a filter assembly.  It will be used in front of a wideband SDR receiver such as the RX888 or the KiwiSDR.  With the typical antenna system and receiver location, the signals at the lower end of the HF range can be quite strong, and at the upped end additional anti-aliasing is often needed (especially when the SDR ADC sample-rate is reduced (down to perhaps 60 MHz).  So the structure is an input high-pass  RLC "shelf" filter that starts at about -20 dB under 1 MHz, then transitions to -1dB above 20 MHz.  This feeds the preamp, which drives a four-section elliptic low-pass filter that essentially brick-walls above 30 MHz.  I've got boards in service now that just contain the filters, and they work very well.  The amplifier is something new.  The SDRs tend to be a bit deaf at the high end of the range, and the 1dB or so filter loss doesn't help.  People are using external preamps, so this new design should simplify things.

I believe that in this application noise figure is less critical than dynamic range, but it's obviously going to be a compromise.

I built a second amplifier using a 2.2 Ohm emitter resistor, and a 560 Ohm feedback resistor.  This simulates out at about 43 Ohms input R, which is OK.  I can still tweak those values, but I used the parts I had on hand.  The measured gain at 10 MHz is +19 dB, measured IP3 is about +25 dBm, and the 1dB compression point is -8dBm.  The -3dB frequency is 182 MHz,

Now I get to solder down the filter components and see how it all plays together.  That elliptic filter Z gets squirrely above the cutoff frequency, so we shall see how the amplifier reacts.  With resistive terminations the amp by itself shows no oscillations, at least not up to 1 GHz,  I will check higher as well.  The board has a moderately tight surface-mount layout, but the components are 0603 or bigger and are not placed too tightly.  It;s a 2-layer board.