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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
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#12
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
"John (Liberty) Bell" wrote in message
... wrote: In the meantime try plotting a graph of SNR versus load resistance for a given source resistance. Remember for a given bandwidth, the noise power is independent of the resistance hence noise voltage varies as the sqrt of the resistance. I am not sure that I see the point of this exercise. The noise generated in a reasonably designed amp is primarily due to transistor noise. Obviously if you could only suppress the input resistance thermal noise then internal sources become more important, but since they are thermal too I am assuming your method would work equally well on both. Whatever the transistor noise, minimising that due to the input resistance remains desirable and since we aren't discussing your technique, I am restricting myself to the question of matching since that can be resolved. Even if it was due to the amplifier's input resistance (i.e. the load seen by the source), this makes no difference. The device supresses amplifier noise, period. Cool ;-) Now to the question of the source. Assuming it absorbs all incident energy, the signal power is V^2 / R . The signal voltage is thus sqrt (incident power x R). However, if the noise voltage is also proportional to sqrt R, the source resistance makes no difference to s/n ratio. The same happens if you perform the corresponding calculation for signal current and noise current. If we ignore e.g. transmission line reflections due to mismatching then, whatever that source resistance, the signal voltage at the amplifier input is obviously maximised when that load resistance is infinite. Conversely, the signal current is maximised when that load resistance is zero. If we don't ignore e.g. transmission line reflections due to mismatching, then this becomes your field not mine. We both know that maximum power transfer is achieved when the source resistance and load resistance are equal. However, I am not so sure that this rule can still be relied on at the two limiting cases where (a) we are driving an idealised amplifier input stage which only amplifies voltage (without requiring any current), ... Ok, let's go into this in more detail. Consider a signal source of voltage Vs and impedance Rs which is fed to an amplifier giving an output Vo. For a high impedance design using a fet or HEMT, we can model the amp as a perfect voltage amplifier with a parallel input resistance: Amp (Vs)--[Rs]--*--|-- Vo | [Rp] | === Gnd By putting a transformer in front of the real amp (not shown), we can make the actual resistance look like any value for Rp we choose, so what is the best Rp? First consider Rp Rs. The current from the load is Is = Vs / (Rs+Rp) ~ Vs/Rp so the operation is almost constant current. The input signal voltage is Vs = Is.Rp The noise power is given by Pn = k.T.B where k is Boltzmann's constant, T is the temperature in Kelvins and B is the bandwidth in Hz. The power in a resistor in general is P = V^2/R hence the voltage is V = sqrt(P.R) The noise voltage is therefore Vn = sqrt(Pn.Rp) = sqrt(k.T.B.Rp) For Rp Rs, as we vary Rp the signal voltage varies in proportion while the noise voltage varies as the square root. That means if we quadruple Rp, the signal voltage will increase by a factor of four while the noise voltage only doubles hence increasing Rp will improve the SNR. Now consider Rp Rs. The current from the load is Is = Vs / (Rs+Rp) ~ Vs/Rs so the operation is almost independent of Rp. The noise voltage is still is proportional to the square root of Rp so now any increase in Rp has no effect on the signal voltage presented to the amp but does increase the noise. For Rp Rs, we can improve the SNR by decreasing Rp. Put those two together and clearly there will be a maximum of SNR somewhere between Rp Rs and Rp Rs and it turns out that maximum occurs at Rp = Rs. ... and (b) we are driving an idealised amplifier input stage which only amplifies current (without requiring any voltage). Perhaps you could tell me the answers, in those two limiting cases. This case is more complex. V Amp (Is)--*--[Rs]--|-- Io | \ [Rp] \ | \ === Gnd Virtual earth Now we have a current source in parallel with Rp. The amp is controlled by current into the virtual earth point and it produces a proportional output current Io. Power in a resistor is I^2.R but in this case the noise power in Rs is dissipated in both Rs and Rp (the noise looks like a current mode generator across Rs). Alternatively the noise current in resistor Rs is In = sqrt(Pn/Rs) For the case Rs Rp, the situation is simple. Almost all of the signal current enters the amp so it is independent of Rs but the noise is mostly dissipated in Rs hence as Rs is reduced the noise current increases as the inverse square root and the SNR gets poorer. For Rs Rp therefore we can improve SNR by increasing Rs. For Rs Rp, the thermal noise from Rs is mostly dissipated in Rp as is the signal current Is. The voltage V therefore is substantially independent of Rs for both noise and signal and the SNR tends towards the ratio of the source power to the noise power in Rs asymptotically. The resulting conclusion is that the higher Rs the better. In other words, if you have a 50 ohm source, the best series resistor in front of your current-input amp is many megohms! Clearly this isn't right. What I think is missing from this picture is that the output current has to be changed back to a voltage to be useful by feeding Io into a resistor. It needs to be proportional to Rs for a given gain and the noise from that resistor will then increase as Rs increases producing an optimal value for Rs. That raises the question of whether such an amp fed into a current-input DAC but give the best noise performance but in transistor amps, the base spreading resistance creates a practical limit and we were talking about HEMT amps anyway. George |
#13
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
[Mod. note: entire quoted thread removed -- mjh]
I apologize in advance, but I haven't taken the time to read this entire thread. So hopefully I won't repeat something already discussed. Why approach this problem from the point-of-view of currents and voltages? Why not use S-parameters? Also, for the LNAs that I'm aware of, there is no resitance in the first-stage matching network. Just conductive and inductive impedances. The key is to match the input matching network to the optimal noise match of the first-stage transistor. The trade-off is that this tends to hurt input return losses of the amp, but luckily some inductive feedback will fix that. So, basically you have Noise Figure = Minimum Noise Figure of Transistor + (terms related to impedance matching) Regards |
#14
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
OK I am switching this particular part of the discussion between me and
George to private email now. It is clear that each of us has different areas of specialised expertise, and I think further progress should be more rapid if that part of the discussion is now continued in private. Regards John Bell |
#15
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
Peritas wrote:
[Mod. note: entire quoted thread removed -- mjh] I apologize in advance, but I haven't taken the time to read this entire thread. So hopefully I won't repeat something already discussed. Why approach this problem from the point-of-view of currents and voltages? Why not use S-parameters? Also, for the LNAs that I'm aware of, there is no resitance in the first-stage matching network. Just conductive and inductive impedances. Quite. What we started discussing, before simplifying matters, was the internal capacitance of the transistor gate, the resistance to which that connects internally, and the desirability of achieving impedance matching of that with the source impedance. The reason we switched to discussing pure resistances was that George pointed out that correct choice of inductors would cancel out capacitance at the designed centre frequency, thus leaving pure resistances to worry about for impedance matching. The key is to match the input matching network to the optimal noise match of the first-stage transistor. The trade-off is that this tends to hurt input return losses of the amp, but luckily some inductive feedback will fix that. This raises an interesting point that I was wondering about. If we consider, for simplicity, the idealised situation where the input transistor is replaced by an op amp, then the ratio of negative feedback Z / souce Z, not only defines the gain, but also reduces the effective input resistence at the inverting amplifier terminal to zero (virtual earth). How does that consequence of negative feedback affect the impedance balancing we have been discussing? John |
#16
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
Peritas wrote:
[Mod. note: entire quoted thread removed -- mjh] I apologize in advance, but I haven't taken the time to read this entire thread. So hopefully I won't repeat something already discussed. Why approach this problem from the point-of-view of currents and voltages? Why not use S-parameters? S-parameters typically assume the input and output ports are terminated in matched loads while we are discussing the loading to optimise the SNR for a given source impedance. S-parameters also don't address the question of thermal noise directly. Also, for the LNAs that I'm aware of, there is no resitance in the first-stage matching network. Just conductive and inductive impedances. In my experience, those components are arranged to cancel the reactive part of the active component input impedance to leave a resistive load. The key is to match the input matching network to the optimal noise match of the first-stage transistor. The trade-off is that this tends to hurt input return losses of the amp, but luckily some inductive feedback will fix that. So, basically you have Noise Figure = Minimum Noise Figure of Transistor + (terms related to impedance matching) Yes, that is conventional (for good reasons) but the question John is asking is whether, if we are prepared to tolerate a high value of S11, we can get a small improvement in SNR when considering only the limiting thermal noise in the real part of the input impedance. best regards George |
#17
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
John (Liberty) Bell wrote:
OK I am switching this particular part of the discussion between me and George to private email now. ... I am discussiing the topic with John by email but I thought these two papers may be of wider interest as an indication of the level of detail that current "state of the art" work considers (or at least the state a few years ago). While our discussion has been mainly at a theoretical level, real world limitations of component manufacture is a prime driver of the amplifier design. http://www.imec.be/esscirc/esscirc20...gs/data/76.pdf The following also discusses "themal noise canceling" though perhaps not in the sense that John means: http://amsacta.cib.unibo.it/archive/...1/GA043200.PDF George |
#18
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
wrote:
John (Liberty) Bell wrote: OK I am switching this particular part of the discussion between me and George to private email now. ... I am discussiing the topic with John by email but I thought these two papers may be of wider interest as an indication of the level of detail that current "state of the art" work considers (or at least the state a few years ago). While our discussion has been mainly at a theoretical level, real world limitations of component manufacture is a prime driver of the amplifier design. http://www.imec.be/esscirc/esscirc20...gs/data/76.pdf The following also discusses "themal noise canceling" though perhaps not in the sense that John means: http://amsacta.cib.unibo.it/archive/...1/GA043200.PDF George Although these papers were both interesting and potentially relevant in their own right, there are several additional points I think worth mentioning. In specific relation to http://amsacta.cib.unibo.it/archive/...1/GA043200.PDF, although the authors claim to be describing a CMOS LNA in the abstract, it turns out in the paper that they have only described NMOS and bipolar in practice. For those who don't understand the difference (which appears to include these authors), a CMOS amplifier (or digital switch) stage comprises the conductive channels of an n type and a p type MOSFET connected in series (typically across the power rails), whilst their respective gates are connected in parallel, such that when one is switched on, the other is switched off, with a mutually conductive (approximately linear) region there between. Having said that, I note, more importantly, from section C of this paper: A) That impedance matching and noise minimisation are indeed not the same thing, as I suggested in a recent response from me to George. B) That negative feedback can and has been employed to break this trade-off (as I already had in mind [as fine detailing] within a practical implementation of my design) C) That global negative feedback will indeed change Zin, as I suggested was also an important consideration in my response to Peritas. Finally I can confirm that George was correct in guessing that these papers have nothing to do with my central noise suppression proposal. Nevertheless, I cannot currently see why such methods could not be used in conjunction with that proposal, if desired. John Bell (Change John to Liberty to bypass anti-spam email filter) |
#19
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
John (Liberty) Bell wrote:
Peritas wrote: [Mod. note: entire quoted thread removed -- mjh] I apologize in advance, but I haven't taken the time to read this entire thread. So hopefully I won't repeat something already discussed. Why approach this problem from the point-of-view of currents and voltages? Why not use S-parameters? Also, for the LNAs that I'm aware of, there is no resitance in the first-stage matching network. Just conductive and inductive impedances. Quite. What we started discussing, before simplifying matters, was the internal capacitance of the transistor gate, the resistance to which that connects internally, and the desirability of achieving impedance matching of that with the source impedance. The reason we switched to discussing pure resistances was that George pointed out that correct choice of inductors would cancel out capacitance at the designed centre frequency, thus leaving pure resistances to worry about for impedance matching. Well, from my point-of-view, this is how I think of the initial steps to designing an LNA. (Incidentally, I think this post will address some of George's comments that he made independently in response to my "s-parameter" post mentioned above.) 1. Obtain an s-parameter model and noise model for the FET that you plan to use. You can then take this info and use it to plot the optimal input return loss (IRL) match of the FET and the optimal noise match of the FET on a Smith chart. All of the internal resistances, inductances, and capacitances of the FET are included in this information. 2. For an LNA, one starts with the input stage matching network. You know that there will be a 50ohm load connected to the input of the entire amp (unless a different load is spec'd), and by this point, you know what load you need to present to the 1st stage FET to get a good IRL and a good noise figure. Now, the first problem is that the optimal IRL match will not be the optimal noise match. In many cases, a shunt inductor hanging off the FET's source pads is used to pull these two points closer together on the Smith chart. 3. At this point, one can start using capacitors and inductors to match the outside 50ohm load to the IRL/Noise load(s) of the FET (which are now closer together, but still not on top of each other). 4. Of course, one must consider stability, gain, and whatever else is spec'd by the end-user. Also, once one adds stages after the 1st stage FET, some of steps 1-3 will need to be re-tweaked b/c the FET's isolation is not infinite. Oh, and one does not want to through away gain in the first stage. The noise contribution of subsequent stages is reduced by the amount of gain in the first stage! The key is to match the input matching network to the optimal noise match of the first-stage transistor. The trade-off is that this tends to hurt input return losses of the amp, but luckily some inductive feedback will fix that. This raises an interesting point that I was wondering about. If we consider, for simplicity, the idealised situation where the input transistor is replaced by an op amp, then the ratio of negative feedback Z / souce Z, not only defines the gain, but also reduces the effective input resistence at the inverting amplifier terminal to zero (virtual earth). How does that consequence of negative feedback affect the impedance balancing we have been discussing? John I'm not sure how to answer this question specifically, but does step #2 help by analogy? Remind me now. What is the original purpose/intent of this thread? Maybe my answers regarding LNA design are too generalized. Regards |
#20
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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )
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