Grounding the Grids vs. Cap/RFC Grounding

Discussion in 'Amateur Radio Amplifiers' started by W4LAC, Jun 13, 2019.

ad: L-HROutlet
ad: l-rl
ad: L-MFJ
ad: Left-3
ad: Subscribe
ad: Left-2
ad: MessiPaoloni-1
  1. G0HZU

    G0HZU QRZ Member

    Yes, the latest generation of engineers are exploiting these new devices in exciting ways. I guess the reason I described it as a bit sad was because (in lots of areas) the modern chipsets/DSP are creating a layer of insulation between modern RF design techniques and basic physics.

    Maybe a few forum readers will be a bit alienated by my references to 'negative resistance'. Most people are quite comfy with the physics behind regular resistors and 'resistance' but the concept of negative resistance may be a bit of a mind bender for some. But in reality it isn't anything exotic. We have all measured FWD and REV with a VSWR meter when measuring antennas and antennas are usually passive devices. So the worst case 'reflection' is usually one where the antenna isn't there or is broken and the VSWR appears to be infinite. In this case the reflection coefficient is 1 (or extremely close to 1) because the reflected wave is the same size as the forward wave.

    Negative resistance can occur in active devices like amplifiers and when the VSWR of an amplifier port is measured with a VNA the reflected reading can arrive back slightly bigger than the initial forward reading. This means the load under test is an active source that can boost the strength of the reflected signal and it is said to be generating negative resistance. The magnitude of the reflection coefficient might be 1.015 for example. This is only a tiny amount bigger than 1.000 but this is enough to cause instability in an amplifier if it is then presented with a passive load impedance that can set up a series LCR network where the negative resistance produced by the amplifier is able to dominate the passive resistance in the passive load network at a frequency where there is resonance. In this case the resonance happens just outside the regular smith chart and this is the region where negative resistance can be plotted on a VNA.

    A modern VNA will be all set up to cope with and display negative resistance although the smith chart display may have to be shrunk to allow extra screen space to display the region outside the regular smith chart circle where the negative resistance is occurring. All areas inside the regular smith chart circle are impedances that have positive resistance.
     
    Last edited: Jun 18, 2019
  2. G0HZU

    G0HZU QRZ Member

    The next stage is to consider what this can mean in the real world. Take a look at the first Spice simulation below. In this case, energy is initially stored in the inductor via the switch and then the switch is released. Once this happens the switch becomes invisible. When this happens the stored (magnetic field) energy in the inductor starts sloshing back and forth between the inductor and the capacitor (in the electric field) and this causes oscillation at the resonant frequency at about 173MHz. This is a the classic resonant tank circuit that we all know so well. However, because the inductor has a finite loss resistance of 2 ohms this 173MHz oscillation is damped and it quickly dies away.

    But suppose the 5pF capacitor was in series with a negative resistance of -5 ohms. The second Spice simulation shows what happens... the oscillation now grows and grows out of control because the -5 ohm resistor dominates the 2 ohm resistance of the inductor. If the -5 ohm resistor had been a -2 ohm resistor then the oscillations would have stayed at a constant level forever.

    A simple analysis of a JFET (or an RF tube) will show that up at VHF it can generate a negative resistance of maybe -10 ohms. This will be in series with the tube (or JFET) capacitance of maybe 5pF. So the above numbers are quite relevant in this case.
     

    Attached Files:

  3. G0HZU

    G0HZU QRZ Member

    The next stage is to add a parasitic suppressor as in the image below. I've left this at 47R and 85nH even though this probably isn't the ideal design here. The equivalent series resistance of this suppressor is over 35 ohms at 170MHz and the series inductance is about 20nH as in the first graph below.

    This is more than enough to offset the -5 ohms at 170MHz and there is a very heavily damped output. So it is very stable now. However, the extra series 20nH will bring the resonance down to about 163MHz and the marker shows the series resistance of the suppressor is 36.5 ohms here. There is also 2 ohms in the inductor. So for the system to 'just' go unstable again at 163MHz it would have to now generate -38.5 ohms negative resistance and this is shown the second plot below. If it generates -35 ohms the oscillations will be damped away and if it generates -40 ohms the oscillations will grow rapidly. But -38.5 ohms should give an almost constant oscillation level and the second plot below shows that the circuit is right on the stability limit if the negative resistance could ever get to -38.5 ohms at 163MHz.
     

    Attached Files:

    Last edited: Jun 18, 2019
  4. G0HZU

    G0HZU QRZ Member

    In brief, the suppressorZ plot in the post above shows that (at 80MHz and above) the equivalent series resistance of the 47R and 85nH parallel suppressor can 'protect' against an amplifier that can generate a negative resistance of up to maybe -20 ohms or so up at these frequencies. By 200MHz it can protect up to nearly -40 ohms of negative resistance in an amplifier. The next stage is to look at the datasheet for a JFET (and a tube) and do a few simple sums to predict just how much negative resistance we can expect to see from a real amplifier. It will depend a lot on the grid inductance and the internal capacitance of the device and also its transconductance. I might not be able to do this stuff tonight but for the JFET case I hope to show you a pen and paper prediction, a computer simulation using the datsheet model and also a VNA measurement of a real device to show the negative resistance it generates up at VHF. Then a suitable suppressor can be evaluated to see how it improves things.
     
    Last edited: Jun 18, 2019
  5. G0HZU

    G0HZU QRZ Member

    To give an idea of what to expect if an amplifier with 5pF capacitance and -15 ohms of negative resistance is tested with a VNA, the plot below shows the reflection coefficient for 5pF in series with a negative resistance of -15R. The smith chart plot shows that at 163MHz the reflected wave from the amplifier will be 1.037 times bigger than the incident test wave. This is a tiny difference but it is hugely significant. It will be reflected with an angle of -28.5deg and this angle is mainly caused by the capacitor. If the negative resistance was reduced to zero the reflection coefficient would be 1.000 with an angle of about -28.7deg. So the capacitance dominates here.

    You can see that the VNA trace has crept outside of the regular smith chart circle and this is a sure sign of negative resistance in the device under test assuming there are no measurement or VNA calibration errors.

    The 1.037 reflected wave can be thought of as providing a tiny sniff of extra energy that can top up a resonant tank circuit to overcome its passive losses. So you get a growing oscillation in the resonator rather than the damped oscillation you would see with a purely passive and lossy circuit. So this forms the basis of an unwelcome oscillator and the oscillations will build up and up until the limit of the tube is reached and the oscillation will either level off to a fixed amplitude or the amplifier might fail due to overvoltage issues.

    To measure this 1.037 reflection coefficient correctly requires a decent VNA and some operator skill. Otherwise, the negative resistance might be missed if the VNA is calibrated poorly or if it is a low performance VNA.
     

    Attached Files:

    Last edited: Jun 18, 2019
  6. G0HZU

    G0HZU QRZ Member

    To make the above circuit oscillate at 163MHz you would just need to add a series inductor with enough reactance to cancel the -28.5degrees caused by the capacitor. This would create resonance. This would require a 190nH inductor to make up the tank circuit. It will oscillate as long as the ESR of the inductor is less than 15R at 163MHz.
     
    K2XT likes this.
  7. HAMHOCK75

    HAMHOCK75 QRZ Member

    Nice presentation. I suspect you may have gone well over the heads of the vast majority of hams. I once mentioned on a thread about designing amplifiers with a vector analyzer and S-parameters. Probably my best response was "never heard of S-parameters". My first job out of college was at HP. My first day on the job, they sat a vector network analyzer next to my desk.

    The problem for many is that Smith charts, negative resistance, S-parameters are hard concepts to get your arms around. Most hams think in terms of there is feedback capacitance from point A to point B, etc. The concepts of S-parameters and negative resistance removes that feel about what is actually going on. I suspect if you use these concepts then you know they became necessary because at higher frequencies, there is so much going on that describing things in terms of lumped parameters becomes a nightmare. Also, someone inconveniently invented one port devices like the tunnel diode which have negative resistance but are harder to model in terms of feedback.

    I had a college course which included S-parameters. It can be shown that S-parameters relate to all other sets of parameters, h, y, z, etc. but basically if you can measure the four S-paramenters, S11, S21, S12, S22 you have fully characterized the device including its stability whether conditional or unconditional.

    I think of the Smith chart as representing all real impedance including all values of resistance from 0 to infinity ohms. If a device ever goes outside the chart, it has negative resistance which means the device is conditionally stable. If it never leaves the standard Smith chart it is unconditionally stable. As you illustrated in your last post, conditional stability means there will be some load that will cause oscillation.

    I also read your posts in the thread mentioned by KM1H. You were right there too but I suspect most hams have no idea where you are pulling these numbers from. I also worked in the spectrum analyzer group and these numbers are the bread and butter of analyzer designers.

    The -174 dBm is thermal noise power in a one Hz bandwidth and comes from 10 long ( ktb * 1000 ) where k is Boltzmann's constant of 1.38 E -23, k is degrees in Kelvin, b is bandwidth in Hz, and the 1,000 is to convert to dB relative to a milliwatt ( dBm ). So from that formula, increasing "b" by a factor of ten increases thermal noise power by 10 dB. Therefore thermal noise in 10 Hz bandwidth would be -164 dBm, in a 100 Hz bandwidth, 154 dBm, in a 1 kHz bandwidth -144 dBm, etc.
     
  8. G0HZU

    G0HZU QRZ Member

    Thanks. Maybe this would be better presented in a youtube video but I'm not a great presenter and my video editing skills are even worse. I'm running out of time tonight but I did build a test circuit using a J310 JFET and I did produce two datasheet based models. One was analysed using Genesys and the other was analysed using Simetrix. I went for 9nH gate inductance, Cgs of 4.3pF and Cgd of 1.8pF and a transconductance of 12mmho. These are straight from the J310 datasheet. However, to make the device more like a tube I padded the Cgd with an external 3.3pF for both the models and the real circuit. This boosted the net series capacitance to just over 5pF to be more like an RF tube.

    The crudest model was just based around a 12mmho VCCS plus the above data and this predicted a negative resistance of around -15R across the VHF band. The quality of the drain bias choke is critical here as it has to appear invisible and it must not load the output resistively or the negative resistance will be affected. Ideally, this should be done via a VNA bias tee but I didn't bother. When I measured the real circuit with a VNA the results were still good and agreed well with the models as in the plot below. The dark trace is the negative resistance vs frequency for the real circuit and the red trace is for the model.

    Anyone can repeat these tests and they should get similar results.

    See below for the negative resistance seen at the drain of the JFET. The two traces are for the VCCS model (derived from the datasheet) and a measurement of the real circuit on a VNA. This shows fairly good agreement and this shows about -15R negative resistance across a wide bandwidth.
     

    Attached Files:

  9. G0HZU

    G0HZU QRZ Member

    The purpose of the above was to demonstrate that you can get a reasonable idea of the negative resistance that a grounded gate (or grid) amplifier will produce if you look at the datasheet and also have a good idea of the gate/ grid inductance.

    The other tests I did with the real JFET circuit was to add an 82nH SMD inductor as a load. Because the model and the VNA predict about 5 or 6pF in series with -15R this circuit can be expected to oscillate up at around 230MHz because this is the resonant frequency of the 82nH in series with just under 6pF. I used an accurate Coilcraft 82nH inductor and the picture below shows that it does oscillate up near 230MHz. I then added a 15R series resistor with the 82nH inductor and the combined ESR of the 82nH inductor and the 15R resistor should just overcome the -15R negative R in the JFET and so the circuit should not oscillate. When I fitted this 15R resistor it stopped oscillating and this is to be expected. But if I replaced the 15R with a 12R resistor it started oscillating again. This is because there is probably a net negative resistance of about -2 or -3 ohms and this is enough for oscillation to start up. This is a fairly good test to show the validity of the modelling and the VNA measurements.
     

    Attached Files:

    Last edited: Jun 19, 2019
    K2XT likes this.
  10. G0HZU

    G0HZU QRZ Member

    I'm out of time tonight but here is an initial crude datasheet based estimate of the negative resistance of the 500Z tube across frequency when in grounded grid. Because I don't have one of these here to play with I've had to guess the total stray grid inductance at 7nH. Everything else is straight from the datasheet. It predicts just under -10 ohms of negative resistance across VHF. Of course, this is really just the equivalent of a 'first page' model in a logbook and it would need refining. For example, if I fit a LPF with shunt capacitance at the cathode then the negative resistance creeps up to nearly -10R but that isn't shown in the plot below. Also there will need to be tweaks to the model to account for the physics of the tube itself as it is such a large structure. The 'best' way to create an accurate 1 port model would be to measure the real tube with a VNA but this would be extremely hazardous because of the lethal voltages inside this amplifier. Also the test gear could get toasted! But such a measurement would provide an accurate 1 port (small signal) model at the anode with no need to guess anything like the grid inductance. It would provide a much better version of the plot below. However, I don't recommend anyone tries this as it would be very dangerous.

    Alo included in the image below is a plot of the Rollett stability factor K and also a plot of B1. Together these can be used to assess if the amplifier is unconditionally stable at the (initial) small signal level. The plot shows this model is nowhere near being unconditionally stable as K dives below 1 above a few MHz. B1 dips below zero too. This is mainly because of the negative resistance and this is not good. However, nothing has been added to try and tame it (like a adding a suppressor for example).
     

    Attached Files:

    Last edited: Jun 19, 2019

Share This Page