Oct 27, 2015

This article describes a noise-measurement system with an effective bandwidth of 550kHz or 100kHz. The system can be used to measure total output noise of circuits with output impedances below about 100ohm. A Midiman DMP3 high-gain very low noise preamplifier is used to amplify the broadband noise signal (from 3Hz to about 550kHz or 100kHz) from the circuit to be tested. The noise output of the preamplifier is measured using a Digilent Analog Discovery 10MHz scope and measuring AC rms volts. The configuration is shown below:

It is important to understand how the preamplifier input and output RC filtering might affect this measurement bandwidth. In this setup, a plug used with the balanced input reduces the input to single-ended with an input resistance of 100kΩ in parallel with about 50pF capacitance (from schematic diagram). However, the circuit to be measured (DUT) has an output resistance of at most 100ohm typically which shunts the higher input resistance. In addition, a 2' coax cable with a capacitance of 60pF was used between DUT and the DMP3. This creates an input low-pass pole with frequency no lower than 100ohm&110pF or 14MHz. Therefore this input pole for this setup does not affect the measurement bandwidth significantly. Similarly, the output resistance of the DMP3 final stage is 470ohm. Again the DMP3 output is connected to the scope with a 2' coax cable and the input capacitance of the scope is 25pF. Therefore the output pole filter frequency is 4MHz, again well beyond the measured "noise bandwith" of 550kHz.

With the shielded box connected to the DMP preamp as described above (but power turned off to the DUT) , the measured rms output noise floor for the setup was ~ 2.0 mV corresponding to an effective DMP3-input total noise voltage (in the 550kHz noise bandwidth) of 2.0/1160 = 1.7µV, slightly higher than the noise voltage measured with the scope disconnected completely. Therefore, this configuration can be used to measure DUT total output noise voltages in this bandwidth down to about 5µV without this background noise floor affecting the results significantly:

Noise measurement results are shown below for the following basic transimpedance photodiode circuit with a 16MHz OPA627 op-amp. The BPW24R Si PIN photodiode has a bandwidth of about 40MHz (when reverse biased) with a zero-bias capacitance of about 11pF. The extra 220pF shunt capacitance was added to conveniently study effects such as circuit stability dependence on photodiode capacitance:

With the photodiode in the dark, the scope noise voltage was 20mV corresponding to a total output noise voltage for the transimpedance circuit of 20.2/1160 = 17µV in good agreement with the 20µV integrated total output noise calculated for this circuit in a 550kHz noise bandwidth. The total output noise for this circuit in this bandwidth is dominated by the amplified

Increasing the total shunt capacitance across the photodiode to 1220pF causes the well-known increased noise-gain amplification for

Finally, the photodiode was illuminated with an LED. The LED was powered by a separate battery power supply and filtered. An output DC level of 2.88V was measured corresponding to a photocurrent of 96µA through a 30kΩ feedback resistance. For this measurement, Cd=220pF as for the first meaurement above:

In this case, the transimpedance circuit output noise of 92.6/1160=80µV is dominated by the photocurrent shot-noise, in reasonable agreement with the calculated total noise of 68µV.

The Butterworth circuit design above assumes an ideal voltage source with zero resistance. However, the output of the DMP3 has a 470Ω series resistance from the final op-amp output stage. Therefore, to maintain the proper Butterworth filter design when used at the DMP3 output, the input resistor of the Butterworth filter must be lowered to (1250-470) = 780Ω. The response of the combined system DMP3 + 90kHz post-filter is shown below along with the response without the filter. Noise measurements of the sample circuit above, are consistent with the calculated total noise for the smaller 100kHz noise bandwidth. For a simplified assumption of frequency-independent noise spectral density and noise amplification, and with the total noise scaling as √NBW, one expects the noise for the 550kHz filtering to be about ~ 2.35x higher than the 100kHz filtered value. However, more accurate estimates of the total output noise must take into account that the different noise sources can be amplified with different spectral profiles:

A convenient switching arrangement was used enable/bypass the 100kHz post-filter circuit, as shown below:

- thermal noise of Rf,
- op-amp current noise <in>
- op-amp voltage noise <en>
- signal photocurrent shot noise

To demonstrate the gain profiles, the plots below which don't include the post-filtering used in the measurements, are accurate simulations of the transimpedance functions Tz(f) (actually |Tz(f)|), and noise gain functions |NG(f)| for the circuit measured above for two different Ci values of 220pF and 1220pF. For this circuit, it can be shown that the TOTAL (integrated over ALL frequency, Fmax-->infinity) output noise due to Rf, <in> and signal shot noise are independent of Ci (for fixed Rf, Cf and GBW), even though the Tz(f) transimpedance function changes shape as shown. (This is NOT true for the cumulative total noise for these sources up to some arbitrary finite frequency Fmax). However as Ci is increased, the total amplified op-amp voltage noise <en> increases greatly as shown, eventually being attenuated by the finite GBW rolloff of the op-amp. It is for this reason that in transimpedance circuits, particularly with higher Rf values, it is important to choose an op-amp with very low voltage noise <en> and minimize Ci if possible:

The frequency response of this circuit is shown below with an f-3db of 10MHz:

The total output rms noise voltage and FFT spectrum is shown below, using the DMP3 amplifier configuration described above with a noise-bandwidth filtering set at 550kHz. Assuming the spectral noise density functions for en, in and thermal noise of Rf are frequency independent (except for low frequency 1/F noise), the output spectral noise density will be constant with frequency over the full bandwidth of this amplifier and will roll-off as the circuit gain above 10MHz. Since the DMP3 amplifier circuit post-filters noise with an effective NBW of 550kHz, the amplified output spectral noise will be uniform below this NBW. This is demonstrated in the FFT spectrum below where the rolloff around 550kHz is evident:

The scope real-time display measurement shows an amplified total noise within this NBW of 216mVrms or -13.3dBV. Since the DMP3 midband circuit gain is 1160, the LT1226 amplifier output noise voltage is 216mV/1160 = 186µV or -74.6dBV. This compares well with the calculated total output noise in this NBW of 197µV. This noise is dominated by amplified

The FFT plot shows a noise level of -37dBV. This refers to the noise within the frequency bin of the FFT sampling and is further increased by filter shape used in the FFT sampling. To scale the FFT vertical scale to the more conventional power spectral density PS units

To verify consistency, in the passband of the circuit, the op-amp input noise voltage

in agreement with the FFT converted value.

Note that in this NI amplifier example, the spectral noise density is fairly flat until the filter rolloff. There is no noise-gain peaking as is evident from the frequency response plot. This is because the capacitance at the INV op-amp input is fairly low and the resistance to ground there is small as is usually the case for standard NI voltage amplifiers. In this case, all noise sources (thermal, in and en) are amplified uniformly and are rolled off exactly as the Vs gain function, which in this case is identical to the noise-gain function.

The second example using the transimpedance circuit above but with Cd=1000pF demonstrates a nonuniform spectral noise pattern clearly showing a transition from Rf thermal noise domination, transitioning to