# Amplifying a nV signal across a small resistance

I am interested in the feasibility of amplifying/measuring a nV level (or otherwise assumed very small) signal across a small resistance.

The SNR of this signal isn't so bad in itself because of the very small thermal noise, due to the small value of the resistance. My main concern is that commercially available low-noise amplifiers seem to inevitably add input noise on the level of a few nV per square root hertz, obviously swamping the signal.

Do I have any other option? I was thinking that due to the small resistance, I might not need an amplifier with such a high input resistance, which might partly cause the noise? I'm not sure.

• what's your budget and application? Mar 25, 2017 at 20:53
• Most likely no other options Mar 25, 2017 at 20:55
• @Orhym What is the bandwidth of your signal? Does your signal have a DC component that needs to be preserved ? Mar 25, 2017 at 21:17
• @TonyStewart.EEsince'75 Application is sensing, and budget has to stay reasonable (< \$100). Mar 25, 2017 at 21:24
• @Autistic DC needs not to be preserved. The signal can be assumed to be at a single frequency. Mar 25, 2017 at 21:25

The spectrum of interest is important : some otherwise very good amplifying devices have extra high noise at frequencies below 10Hz.

Two options are worth considering : the first is bipolar transistors to provide useful gain before an opamp second stage.

Why not go straight to an opamp? They are pretty noisy, very few have input noise voltage below 1 nV/rtHz, and you want to do better than that.

PNP transistors are preferred, thanks to their lower base spreading resistance. One example with a good reputation some years ago was the 2SC2547, datasheet still available here...

Looking at the contours of constant noise figure on page 6, which helpfully plot 2dB and 4dB contours, but not the most useful 3dB, so you have to interpolate between them. But the 1 kHz plot shows a minimum in teh noise at Ic=10mA, with 3dB noise figure with a source resistance between 10 and 20 ohms - call it 15 ohms.

That implies that this transistor, at Ic=10mA, can be as noisy as a 15 ohm resistor - at or above 1 kHz. Note curves for 120Hz and 10Hz allow you to choose a different working point if lower frequencies are important.

Johnson noise ( from Wiki) can be calculated as

0.13 * sqrt(R) nV/rtHz.

So, 0.9nV nV/rtHz would be the noise of a 48 ohm resistor, while this transistor (or a 15 ohm resistor) would give 0.5 nV/rtHz.

I have used it in microphone amplifier input stages, in a typical mic amp input configuration (long tailed pair, current source feeding both emitters, 470R or 1K in each collector{ feeding an opamp, and it does what it says on the tin.

Less exotic PNP transistors like the humble BC214 or newer may do reasonably well too.

The second option, if the spectrum of interest doesn't include DC, is a step-up transformer to match your source impedance to the noise impedance of your chosen amplifier.

For example if you choose the NE5534A with 3.5nV/rtHz, or a noise impedance of 700 ohms, and your source impedance is 1 ohm, you need an impedance transformation ratio of 1:700, or a voltage transformation ratio (turns ratio) of 1:26 (sqrt(700).

The transformer's primary resistance is a noise source of course : it should be relatively few turns, and large diameter wire, to keep the resistance (and hence noise) down. The secondary resistance matters too, though its noise is added on top of the stepped up secondary voltage.

FET input amps don't suffer from the same noise sources as resistors, which is how they can still have <100nVpp noise with input resistances in the teraohm range.

Analog devices makes a "32" bit ADC w/preamp with input noise of <100nVpp, you could average out many samples to try to improve the noise floor (5sps for an hour should give you a couple extra bits of "noise free" data).

As for general opamps, the AD8000 opamp has only ~20nVpp noise between 0.1 - 10Hz, that's peak-to-peak noise, not root-Hz.

There's a British company that makes seemingly non-superconducting picovoltmeters! They might have something useful.

Otherwise, see if you can borrow someone's lock-in amplifier. But using one of these is NOT for the feint of heart.

Remember, it doesn't matter what you're doing, there's almost always another way, not necessarily a better way, but you usually have options. The trick is finding them.

• Can you expand briefly on the challenges of using a lock-in amplifier? Mar 25, 2017 at 21:37
• @Orhym Aside from lock-in amplifiers being usually big, expensive and quite complex systems, lock-in amplifiers tend to use an AC excitation waveform to feed the circuit under test. They do this because by using a frequency other than DC, they can control the 1/f noise. But the catch is that your circuit has to either be driven from the lock-in amp or be synchronized (very, very well) with the lock-in amp. Properly setting up and configuring a lab grade lock-in amp can be quite an involved process.
– Sam
Mar 26, 2017 at 21:24

It's not obvious at all to me that 'a few' nV/sqrt Hz noise swamps your signal as you have said nothing about bandwidth. If your bandwidth is very low then there may not be a problem. Note that it is bandwidth not maximum frequency.

Note that the quoted nV/sqrt Hz noise is above the 1/f corner frequency and if your frequency is low then you may have significant contribution from the 1/f noise as well. Chopper amplifiers have much less 1/f noise but often suffer from relatively high white noise.

A lock-in amplifier, a standard piece of kit in many labs, effectively has a very low bandwidth because of the synchronous demodulation. By modulating and demodulating, in some circumstances, you can operate in the white noise region of your amplifier (constant nV/sqrt Hz) rather than at the lower end.

If the signal is above some tens of Hz, and the source impedance low, you can get a boost by using a simple step-up transformer at the input. There will be a Johnson-Nyquist noise contribution from the winding resistance, of course. The transformer with 1:n turns ratio decreases impedance by 1/sqrt(n) and decreases noise by 1/n, ideally.

It's also possible to build an arbitrarily low noise amplifier simply by paralleling 'n' low noise amplifiers and summing the outputs. The input impedance decreases with 1/n and uncorrelated noise decreases with 1/sqrt(n), so 100 amplifiers in parallel would have 1/100 the input impedance and (ideally) 1/10 the noise.

If you happen to have a liquid helium cryostat and some DC SQUIDs available you can get much lower noise levels but your budget won't pay for even a single cable let alone the setup.

• A lockin amplifier will have the thermal noise of the switches. That KT noise will be down converted and folded again and again, to fit within the switching rate. The PLL must work against that floor. Mar 26, 2017 at 7:46

This circuit has 60dB gain at 1KHz, rising to 86dB below 50Hz. Noise Floor < 1nV/rtHz.

Consider a NJFET preamplifier, with DC_blocking inherent because the preamp is RIAA-compensated and turntable wow/flutter should be rejected. This circuit, from the diyAudio.com website (the forum therein is "Simplistic NJFET RIAA"), provides 60dB gain, intended to convert 250 microVolts into 0.25 volts. The SNR for 250microVolts, the output of a MovingCoil cartridge, will be impressive; the home-builders of these circuits (dozens have been built) speak of "music comes at you out of absolute quiet --- no hiss or hum or buzz, even with Power Amplifier gain cranked to maximum."

Given the total lack of PowerSupplyRejection (note the R1 gain set and R10 gain set are tied to 45volt rail, albeit with C5 and C6 for 2nd gain stage and output buffer) for the first gain stage (dual NJFETS with Q3 bipolar cascade to eliminate Miller effect), you'll need to use the appropriate SHUNT regulator:

The developer of the circuits "salas" is also one of the moderators for diyAudio, and probably will be amused if you drop by and ask about using the circuits for sensors other than MovingCoils. The 2SK170 has noise density well under 1nanoVolt/rtHz; some people use 2 in parallel; some people go for 4 in parallel, perhaps with a few ohms in the FET sources to encourage more-equal current sharing even though an extensive part of that forum discusses NJFET measuring and sorting to the 1% level of matching (1/10ma out of 10 or 15mA).

The experimenters write of being pleased with MovingCoils in the 2 ohm to 10 ohm range; the 6 Ohm MC sensors would be 1nV/sqrt(10) or 0.316nV/rtHz. A substantial infrastructure is required to use such low noise sensors; here is one such physical example:

Note the 50Hz power transformer (most of the builders are in Europe) and rectifiers and first CLC filtering is an a REMOTE BOX, with meter-long cables bringing the 55 volts to the LeftRight channel box in the foreground, with Shunt Regulator on extreme left/right and the actual RIAA (note the huge black film capacitors, for minimal musical-coloring from dielectric-compression) Preamps in the middle. Note the heavy aluminum boxes. The bottom is also the heat sinking for the Shunt Regulators. That may be alum or steel? I don't know.

edit Your goal is accurate measurement of 1 nanoVolt. From a very low Zsource. You'll need to run some wires from the "sensor shunt" to the PreAmplifier. Those wires are candidate-paths for all sorts of trash. Every bit of 60Hz energy, of 120Hz energy, for meters around, will explore those wires for useful conductivity. And those black-bricks, switching regs, also need returns paths.

Examine the isolation of a turntable and cartridge. The shielding, the use of a 5th wire (in addition to 4 wires from the LeftRight channel sensors). You need to minimize the use of those 4+1 wires for extraneous energy. Distance may be your only friend. Yet there is hope. Here is photo of "racetrack" power transformer, the prized method for best Efield isolation between 117VAC/220VAC and the rectified raw DC (before entering the ShuntReg):

Note the primary and secondary are on separate coil forms, minimizing the capacitive coupling of power-line trash into the Preamp, that trash then demanding a return path back to the earth ground outside the building, with the wires to the sensor being a portion of the paths explored.

• 1nV/rtHz is pretty good for a FET!
– user16324
Mar 26, 2017 at 11:19
• The "salas" design operates the first NJFET at 10-15mA, with 7 volts on the drain, into a bipolar cascade to avoid hot-electron noise (avalanching) in the NJFET at high (30 volt) Vdrains. As you know, 2 such NJFets would reduce noise floor by 3dB. Apr 1, 2017 at 2:59

On high frequency, use transformer (air core coils) to fight that low voltage problem. As amplifiers, use triodes, they have low noise. Use metal foil or wire-wound resistors, and try to keep them on low temperature.

• The Precision of Center Frequency will affect the AC measurement accuracy. However the OP has not discussed the need for a precise measurement. Mar 28, 2017 at 15:54

If the signal is AC and narrowband then why not use a tuned transformer to get the voltage up to a reasonable level where normal techniques will work?

The transformer has low DCR and hence low thermal noise. If it is well shielded it will be of great benefit.

Here is an OpAmp design, using 1 nanoVolt noise density OpAmps, in Avcl= 60dB and 100dB; stage 1 is DC coupled, to avoid huge capacitors (vulnerable to Efield interference); stage 2 is DC-blocked in the gain-set network; for fun, I've included 10 millivolts of PowerSupply interference in each OpAmp. Result? the SNR is -70dB. Vout is 29milliVolts; thermal noise is 1 volt; power supply noise is 93 volts. [Without power supply ripple, SNR is -31.5 dB]

And here is why the PowerSupply trash comes through so strongly: the OpAmp PSRR is only 80dB (default values) AND the LsRsCs on OpAmp VDD have no impact on 60/120 ripple (the Caps need to be much bigger, and the series Rs at least 10X bigger).

Now add the benefit of a Lockon Amplifer: modeled as 25Hertz bandpass, with Q=100. The SNR improves (with 1nanoVoltPP input) from -30dB to -5dB. Note, in upper right, I clicked off the "Gargoyles" and "PSI". Note also, below SNR/ENOB windows, I set the FOI FrequencyOfInterest value to exactly 25Hz, necessary because of the highQ filter. And I used the LowPass Filter LRC stage, so I could place the LC resonance exactly at 25.00Hz, using the worksheet; at Q=100 this is necessary.

Here is the noise plot, covering 24 to 26Hz. Notice the many noise sources listed on righthand side, but only the Amplifier Noise and Rg are important. Rg is the 10.01 Ohms to ground, setting the 60dB gain of that Buffered Gain Follower. Again, the Rnoise of the first opamp is 62_ohms, or 1.0nv/rtHz.