Physical limit on BJT amplifier gain? - Page 1
Forum section: electronics / beginners

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 19, 2016, 08:07:24 am
content: Hello all.I am doing some simulations on a common base amplifier built around an RF NPN BJT. I am able to get relatively high voltage gain, but I am beginning to wonder if there is some physical process that the simulator ignores, that may limit the actual gain I can get out of it. For example, feedback might be an issue. How can I go about estimating at which voltage gain the amplifier will be unstable or reach its limit?Thanks in advance!I am attaching a bode plot of the amplifier for your viewing pleasure. Please note that the early knee is acceptable, and comes from having a very high collector resistor.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 19, 2016, 12:51:54 pm
content: With CCS load and very low frequency, Early effect is the only limit. See: hybrid-pi model.At medium frequency, Ccb (plus stray) reduces gain. This can be fixed by canceling it with an inductor, but that only works over a narrow bandwidth. If you don't need much bandwidth, the available gain can be quite high, which makes this valuable in IF (intermediate frequency) amplifiers!For the medium and low frequency ranges, maximum GBW is approximately constant.At high frequency, Cce and stray inductances cause positive feedback, so that your limit is now the maximum stable gain.You can add approximate parasitics to help model this, or try and find a "package parasitics" model for your part (or, maybe you have it already, in which case the gain and phase should be fairly accurate).Tim

author: danadak
author_rank: Super Contributor
timestamp: October 19, 2016, 01:00:23 pm
content: Linvill stability factor one way of establishing.http://rfic.eecs.berkeley.edu/~niknejad/ee242/pdf/ee242_lect6_twoports.pdfhttp://www.nxp.com/files/rf_if/doc/app_note/AN215A.pdfRegards, Dana.

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 19, 2016, 01:52:18 pm
content: Quote from: T3sl4co1l on October 19, 2016, 12:51:54 pmI see! My frequency of interest is 70-120MHz. I assume this is considered to be in the high frequency range? I am mostly worried about positive feedback, and that it may cause oscillations at high gain. Is there any way to minimize this effect, and is the maximum stable gain listed in datasheets? If so, then there is really no need to try and design an amplifier with higher gain than that...Quote from: danadak on October 19, 2016, 01:00:23 pmThanks, I will take a look at this.

author: JS
author_rank: Frequent Contributor
timestamp: October 19, 2016, 04:25:49 pm
content: When working at very high frequency the PCB would also cause an impact, on the GHz region the inductance and capacitance of traces becomes a problem pretty fast. For low frequency the only (or major) factor that may have an impact from the PCB/construction is the resistance added to the emitter.JSPS: even if your freq. of interest is only 100MHz, you need to know it's stable, 1GHz is just one decade above that, so depending on the gain and filtering it may be the problem. Is not uncommon to have trouble over 10MHz in audio circuits. Put a NE5534 (standard high end audio op amp for many years) without external compensation working at unity gain and it will whine at a few MHz, while the freq. of interest for the circuit is 2 orders of magnitude lower.JS

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 20, 2016, 03:51:19 am
content: Yeah, depends on layout more than anything. Like I said, parasitics. If you can model that, you can get a pretty accurate simulation and find out yourself, without even building it (or, you can simply build it and find out -- hope you have a spec. an. with over a 1GHz range though).~100MHz is in the medium frequency range: that lies on the -20dB/dec constant-GBW slope in your plot.If the transistor has a Cout of 2pF, then your desired 50MHz bandwidth (-3dB) requires a load resistance of:R = 1 / (2*pi*BW*Cout) = 1.6kohmSuppose the BJT is biased at 2mA. Then the maximum output amplitude will be 2mA * 1.6kohm = 3.2V (peak, which will come with high IM3 and compression, so you'll want to plan on less signal level than this), or 6.4mW = 8dBm.1.6kohms is kind of high. Use a transformer or matching network to convert it to a more useful impedance, if you need to use it elsewhere, like a 50 ohm output, or to drive another transistor emitter (very low impedance!). Driving another stage, base input, will be pretty close (~kohms), so probably won't need matching. But you may want some damping anyway (unusually small value base-bias resistors?), so that the load resistance doesn't change so wildly with signal level (and with bias, if adjustable -- say for AGC).At 2mA, the emitter input is around r_e = 26mV / 2mA = 13 ohms, which is pretty low. If the source is 50 ohms, you might simply connect a resistor in series (helps linearize). You can use a matching transformer if gain and noise are critical. Beware of Cce feedback, which will act to invert the input impedance. (In one amplifier like this, I found the input impedance to be near -5 ohms, so that series resistance was required, to even get stable operation.)The pure voltage gain is the impedance ratio, 1.6k / 13 = 42dB. But the power gain includes losses and matching, so expect less. 20dB/stage is a very achievable goal, especially if you want a flatter passband.The emitter input impedance is quite low, so that you shouldn't have much worry about the input network bandwidth (even though Cbe is relatively large).The output network must be 1.6kohm || 1.4uH || 2pF (which is Ccb alone, mind you).Other ways to flatten bandwidth include using a bandpass output network. Instead of a single LC resonator, couple two together, enough to get peaks at the top and bottom ends of the band. Since the Q is low (1-2), the theory of coupled resonators doesn't quite apply, and you'll use a traditional series-parallel ladder network style filter circuit instead. To get peaking, specify a Chebyshev type design, with some dB of flatness. The downside is, the series and parallel resonators won't be matched impedances, so you get unequal collector and load resistances -- which may be an advantage, though!Note that the additional phase shift of a high-order filter network affects stability. No free lunch -- you can just tighten up the edges a little. (In the context of wideband amplifiers, the same thing -- peaking -- stands to gain about a factor of 2 bandwidth! But not much more than that, even for high order peaking networks. The returns diminish very quickly.)If you need a relatively high input resistance, and high gain, stability and isolation, consider a cascode stage instead. CE stage feeding CB stage. The noise isn't much worse (despite the huge mismatch of the collector to emitter connection), and you have a much easier time building it.Tim

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 20, 2016, 09:13:55 am
content: Quote from: T3sl4co1l on October 20, 2016, 03:51:19 amThanks for the extremely thorough reply! I am not worried about the output impedance, as it will be fed into a noninverting operational amplifier with an input impedance of several Mohm. The emitter input needs to have as low an input resistance as possible due to the specifications of the signal source (a silicon photomultiplier photon counter), so the lower the better. I am worried about what you mention of the Cce effect. Can you explain how it will invert the input impedance?"The output network must be 1.6kohm || 1.4uH || 2pF (which is Ccb alone, mind you).". Can you explain where you get the inductance value from and why the output network must match the collector network so precisely?

author: danadak
author_rank: Super Contributor
timestamp: October 20, 2016, 10:21:20 am
content: Your load, the NI OpAmp, if it has a stray of 5 pF in wiring and layout, is ~265 ohms at 120 Mhz.Keysight has excellent RF sim tools, free if you qualify -http://www.keysight.com/main/editorial.jspx?gclid=CN3oh9GW6c8CFQx6fgod4XMPiA&ckey=1834446&id=1834446&nid=-34360.0.00&cmpid=zzfindeesof-evaluation&lc=eng&cc=US&s_kwcid=AL!4166!3!132112110736!b!!g!!%2Brf%20%2Bsimulation&ef_id=V8QK2QAABTLcViI5:20161020103031:sRegards, Dana.

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 20, 2016, 10:54:34 am
content: Quote from: danadak on October 20, 2016, 10:21:20 amI can live with that. The resistor is already set to be ~500 Ohm, and the OPA input capacitance is 1.7pF. The stray capacitance that arises from the strip going from collector to OPA input I have calculated to be no more than 1pF, and that is a large estimate compared to the 0.4pF I get from calculating capacitance of a regular stripline. But you are right, I might want to err on the safe side and reduce the collector resistor a wee bit, since this already results in a bandwidth of 117MHz. Probably it will be lower in reality.

author: dannyf
author_rank: Super Contributor
timestamp: October 20, 2016, 11:17:25 am
content: "How can I go about estimating at which voltage gain the amplifier will be unstable or reach its limit?"For DC, it is rc / re where re is both within the device and outside of the device.For ac, it is the lower of that (in impedance) and stability.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 20, 2016, 12:32:58 pm
content: Quote from: Fulcrum on October 20, 2016, 09:13:55 amHuh, is that not an APD but something altogether fancier?Any opportunity to bootstrap it?Quote2pF being the node capacitance, it resonates at midband (95MHz) with L = 1 / ((2*pi*F)^2*C).You can always use a smaller collector resistor, but your gain falls, proportionally of course.Is an op-amp really what you want here? Does the gain really need to be extremely precise? (If so, you need even more gain in this stage, so you can get adequate signal level into the low impedance!)If this is just a signal detection thing, why not use one or two RF amps and couple them directly into the ultimate load (an ADC?)? Sure saves cost and power consumption!Nice thing about your bandwidth is, it fits nicely within lots of good quality baluns, so you can do that, too (I don't know of an ADC this fast that isn't differential input).Tim

author: Zero999
author_rank: Super Contributor
timestamp: October 21, 2016, 07:41:51 am
content: Quote from: Fulcrum on October 20, 2016, 09:13:55 amAs far as your original design is concerned: the gain is around 26dB at the highest frequency of interest so why not use negative feedback to make the gain 26dB at all frequencies up to 120MHz?That seems like a very odd way of doing this. Why not use an op-amp with sufficient bandwidth to give 26dB at 120MHz?

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 21, 2016, 09:23:10 am
content: Quote from: T3sl4co1l on October 20, 2016, 12:32:58 pmA SiPM is an array of thousands of reverse-biased diodes, with a high enough voltage across it to operate in the avalanche region. An incoming photon will set off the avalanche, which is then quenched by a high-valued resistor a few hundred picoseconds later. Very interesting stuff. No idea what you are talking about in regards to the bootstrapping, though.Quote from: T3sl4co1l on October 20, 2016, 12:32:58 pmI would prefer it not to have any overshoot at any frequency, so I won't put inductors in the mix.The reason I am using an op-amp simply this: I'm a noob (or, was more of a noob when I started designing this over a year ago). I had some bad experiences with transistor-based amplifiers and decided to go for opamps which were behaving much more like expected. I now have an opamp-based design that works, and the opamps have been purchased(), so it would be stupid (and take a lot of time) to suddenly change the whole design. If I had the chance, and time, I would probably have done it differently and never touched opamps in the first place. They're expensive!And you are right, itisjust a signal detection thing. The ultimate load is a discriminator, no ADC involved (luckily).Quote from: Hero999 on October 21, 2016, 07:41:51 amNegative feedback where? Opamp, CBA? I cannot use an opamp as the first amplifier stage due to its relatively high input impedance, even when operating in inverting mode.

author: Zero999
author_rank: Super Contributor
timestamp: October 21, 2016, 12:04:30 pm
content: Quote from: Fulcrum on October 21, 2016, 09:23:10 amI was initially talking about the common base amplifier but it shouldn't be necessary, if the gain stage can be implemented with an op-amp.Negative feedback makes the gain uniform across the bandwidth and predictable, rather than very high at low frequencies.QuoteWhy not? If the input impedance is too high, then connect a resistor in parallel with the input.

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 21, 2016, 01:39:59 pm
content: Quote from: Hero999 on October 21, 2016, 12:04:30 pmYou are correct. The input impedance is not the only problem though, as the detector has a terminal capacitance of more than 1000pF. The reason for having a dedicated CBA preamplifier is to shield the consecutive opamp from this high capacitance.

author: Zero999
author_rank: Super Contributor
timestamp: October 21, 2016, 04:07:17 pm
content: Quote from: Fulcrum on October 21, 2016, 01:39:59 pmAnd why do you think the capacitance of the detector will be a problem for the op-amp?

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 24, 2016, 09:23:07 am
content: Quote from: Hero999 on October 21, 2016, 04:07:17 pmYou've got a point. I've been looking through my old notes, and found where I decided op-amps were no good as a preamplifier. It comes down to this:I've got a book, "Techniques for nuclear and particle physics" (W. R. Leo). In this book, there is a chapter on preamplifiers, and it mentions voltage, current, and charge sensitive preamplifiers built around op-amps. For semiconductor detectors, the book eventually says that only charge-sensitive amplifiers will work. I didn't like this due to the long time-constant of a discharging charge-sensitive opamp, which does not fit my requirements. I therefore started looking for alternative solutions, and found this research paper:http://www.sciencedirect.com/science/article/pii/S0168900211020468The first couple of pages touch upon various problems that arises if one tries to use regular amplifier schemes with a SiPM, and shows that a common base amplifier works well. I therefore based my preamplifier design on their findings.

author: Zero999
author_rank: Super Contributor
timestamp: October 24, 2016, 12:12:52 pm
content: I haven't read the paper because it's behind a paywall.Going by the synopsis, it seems like you need a transimpedance amplifier, rather than a simple voltage amplifier which is why the input capacitance is a problem. The input impedance needs to be as low as possible, over the desired bandwidth.

author: StillTrying
author_rank: Super Contributor
timestamp: October 24, 2016, 02:16:23 pm
content: https://www.researchgate.net/publication/257024184_A_fast_preamplifier_concept_for_SiPM-based_time-of-flight_PET_detectors

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 24, 2016, 06:55:29 pm
content: Quote from: Hero999 on October 24, 2016, 12:12:52 pmOh, apologies. I should have checked if it was accessible from outside my university. Please see the reply from StillTrying. If you would read the first two pages and give me your two cents I'd be grateful. I am a bit confused at the moment and could need the opinion of someone with more electronics experience.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 24, 2016, 07:01:57 pm
content: Quote from: Fulcrum on October 24, 2016, 09:23:07 amWhich, by the way, is currently available online as a scan:http://tesla.phys.columbia.edu:8080/eka/William_R_Leo_Techniques_for_nuclear_and_partic.pdfPossibly not intended to be online, given the off-brand HTTP port, but...Copyright early 80s dates it contemporary with AoE1, so we're talking early PCs era here! No wonder they didn't like op-amps!QuoteNote that a CBA is just a cascode, so you get the same charge out the collector, but it's loaded by collector capacitance, not whatever the SiPM's capacitance is, so it can be a huge win for circuits like this.The emitter voltage still wiggles a little, which means the capacitance still matters a little (the time constant is r_e*C), so it's not perfect. But it's a big improvement.How's the SiPM manifest, in circuit? Is it a two-terminal device? Is it on the PCB, or a cable?Tim

author: Fulcrum
author_rank: Regular Contributor
timestamp: October 24, 2016, 08:06:20 pm
content: Quote from: T3sl4co1l on October 24, 2016, 07:01:57 pmYeah it's a bit outdated! But I assumed the principles hadn't changed.The input impedance of the BJT emitter is so low that I haven't given much consideration to its capacitance apart from the usual high-frequency board layout techniques. The SiPM is a two-terminal device, through-hole, mounted physically close to the BJT and given a good amount of decoupling. It also shielded from RF just be sure it's not behaving as an antenna for the signal output from the final amplifier like in earlier designs... Radiative feedback ahoy!

author: StillTrying
author_rank: Super Contributor
timestamp: October 25, 2016, 08:37:43 pm
content: Just to keep the thread alive and well."input impedance of the BJT emitter is so low that I haven't given much consideration to its capacitance"As the signal has to drive it's own 1000pF output capacitance, I don't think the much smaller E-B and E-C capacitances would have much effect.As a random thought, perhaps a small RF transformer could be used to convert the very low impedance pulses to higher impedance, higher voltage pulses with very little loss.