A novel ultra sensitive method for voltage noise ... - Felice Crupi

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where S DUT is the power spectral density (PSD) of the equivalent noise source of the DUT, and S Ci is the PSD due to the EICN of the amplifier i. DUT 1 2 3 4 Spectrum Analyzer Figure 2 – Schematics of the proposed instrument for voltage noise measurements. The DUT can be connected either to one of the two couples of amplifiers or to both couples. The spectrum analyzer performs the cross-correlation between the outputs of any two amplifiers. residual contribution of the (uncorrelated) EIVN of the amplifiers negligible with respect to the DUT noise to be measured. While the above requirements are common to almost all the high sensitivity methods mentioned above, the new method has the very important advantages of not requiring any preliminary characterization of the DUT impedance and of the EICN of the amplifiers and of not relying on the hypothesis of the EICN having a negligible effect. In fact, by using the technique we propose, it is possible to accurately estimate the voltage noise produced by the DUT even in the case in which its impedance is so high that the contribution of the EICN of the amplifiers becomes predominant. Finally we would like to note that by using the very same principle we have developed above, one can obtain similar results by using just three amplifiers instead of four, at the cost, however, of a further measurement step. III. EXPERIMENTAL VALIDATION In order to verify the validity of the proposed method, we have used the four amplifiers configuration shown in Fig. 3. Let now assume that we connect the inputs of the just two other amplifiers (amplifiers 3 and 4) in parallel to the DUT. By evaluating the cross spectrum at their outputs and by taking into account, as before, the voltage gain of the amplifiers, we now obtain for the input referred voltage noise: R2 10k U1 - R1 100 R7 100 R8 10k - U4 S 34 = S DUT + S C3 + S C4 (2) Finally, let us assume that we connect all the amplifiers together to the DUT. In this last case, proceeding as before, we would obtain for the input referred cross spectrum evaluated among any two channels: OP27 R9 R6 10k 1k R4 10k U3 - + + SW1 R10 R5 R3 100k 100 100 C 220nF SW4 - OP27 U2 S 1234 = S DUT + S C1 + S C2 + S C3 + S C4 . (3) OP27 + SW3 D.U.T. SW2 + OP27 At this point it is apparent that we can evaluate the power spectrum of the voltage noise generated by the DUT alone by taking the sum: S DUT = S 12 +S 34 - S 1234 . (4) SW5 6 1 3 2 4 5 R11 1K R12 - 10k U5 It is important to note that this measurement procedure allows to eliminate the contribution of the EICN sources of the amplifiers without requiring the measurement of the DUT impedance and the estimation of the EICN of the amplifiers. The only requirements for this procedure to provide accurate results are that: a) the impedance of the DUT has to be much smaller than the input impedance of the amplifiers used for the measurements; b) the evaluation of the cross spectrum has to be performed using a time record long enough in order to make the R14 R13 1K + + - AD743 10k U6 AD743 SPECTRUM ANALYZER Figure 3 - A simple circuit implementation of the schematics of Fig. 2. 1191
If we take into consideration the case of a single amplifier being connected to the DUT, it can be easily proven that the input referred voltage noise PSD is given by: S tot R1 ⋅ R2 2 = SDUT + 4 KT + Sen + ZDUT Sin (5) R + R 1 where S en and S in are the PSD of the EIVN and of the EICN of the operational amplifier, respectively. Note that the second and third noise contributions, due to the thermal noise of the resistors and to the op-amp EIVN, represent the actual EIVN contribution of the voltage amplifier while the fourth contribution is due to the overall EICN of the voltage amplifier. As discussed in the previous section, the noise sources due to the EIVN of the voltage amplifier are suppressed by the cross-correlation method and the ones due to the EICN can be eliminated by applying the new method. In order to have meaningful measurements, as far as the validation of the new method is concerned, it is appropriate to take into consideration a case in which we have comparable levels for the noise produced by the DUT, for the noise due to the amplifier EIVN and for the noise due to the amplifier EICN. To fall into such a situation, we have chosen an OP27 low-noise amplifier, which is characterized by an EIVN of 3 nV/√Hz at 100 Hz and an EICN of 0.6 pA/√Hz at 100 Hz. Moreover, we used as a DUT the parallel between the series of a resistor R in = 1 kΩ and a capacitor C in = 0.22 µF with a resistor R p = 100 kΩ (fig. 3). Note that we put the capacitor in series with R in in order to increase the DUT impedance at lower frequencies, thus increasing the effect of the EICN, without varying the voltage power spectrum generated by the DUT (see Fig. 4), which in the explored frequency range (f > 100 Hz) is essentially due to the thermal noise of R in . In fact, the resistor R p is needed in order to provide for a bias path to the input of the amplifiers and its value is chosen high enough in order not to interfere significantly with the measurements in the explored bandwidth. S DUT (V 2 /Hz) 10 -15 10 -16 10 -17 2 10 8 10 7 10 6 10 2 10 3 10 4 Frequency (Hz) Figure 4 - Power spectrum of the voltage noise generated by the DUT and squared modulus of the DUT impedance. |ZDUT |2 (Ω 2 ) We followed the three steps procedure described in the previous section. By connecting the channels 1 and 2 to the DUT we obtain: 2 2 12 S DUT + Z DUT Sin 1 Z DUT Sin2 S = + (6) where S ini is the PSD of the EICN of the i-th channel. In the case of channels 3 and 4 connected to the DUT, we obtain: 2 2 34 S DUT + Z DUT Sin3 Z DUT Sin4 S = + . (7) In the case of all the four channels connected to the DUT, we obtain: S + = S 1234 DUT 2 Z DUT Sin3 + Z + Z DUT DUT 2 2 S in1 S in4 + Z DUT 2 S in2 The desired PSD of the DUT signal is therefore evaluated by using Eq. 4. The three measured spectra are reported in fig. 5 along with the extracted PSD of the DUT signal. It is important to underline that although at low frequency the effect of the EICN strongly increases due to the increase of the DUT impedance, the extracted S DUT results quite constant, as it was expected. The average error with respect to the expected DUT thermal noise in the bandwidth between f = 100 Hz and f = 1 kHz, where the EICN is up to 10 dB higher with respect to S DUT , results lower than 10 %. Power Spectral Density (V 2 /Hz) 10 -15 S 1234 S 10 -16 34 S 12 S DUT + (8) 10 -17 10 2 10 3 10 4 Frequency (Hz) Figure 5 – Input referred cross-spectra obtained by connecting the DUT to: a) the first couple of amplifiers, b) the second couple of amplifiers, c) all four amplifiers. The extracted power spectrum of the voltage noise generated by the DUT is also reported. 1192
Page 1: IMTC 2005 - Instrumentation and Mea

A novel ultra sensitive method for voltage noise ... - Felice Crupi

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