*3.5. Noise Testing and Analysis*

The instrument can only measure the output noise power spectrum of the amplifier circuit. The actual noise floor of the sensing system needs to be converted through the transfer function. First, the transfer function of each level, the overall transfer function in Figure 4, needs to be calculated, and the results are shown in Equations (9)–(13) as follows:

$$H\_{\rm circuit}(\mathbf{s}) = \frac{V\_{\rm out}(\mathbf{s})}{V\_{\rm in}(\mathbf{s})} = \frac{V\_{\rm out}(\mathbf{s})}{V\_{\rm sig} + (\mathbf{s}) - V\_{\rm sig} - (\mathbf{s})} = H\_1(\mathbf{s})H\_2(\mathbf{s})H\_3(\mathbf{s})H\_4(\mathbf{s})\tag{9}$$

$$H\_1(\mathbf{s}) = A\_{\upsilon} = (-g\_m \mathbf{R}\_1) / (1 + g\_m \mathbf{R}\_3) = (-g\_m \mathbf{R}\_2) / (1 + g\_m \mathbf{R}\_4) \tag{10}$$

$$H\_2(s) = (-s\mathbf{C}\_1\mathbf{R}\_{11})/(1+s\mathbf{C}\_1\mathbf{R}\_7) = (-s\mathbf{C}\_3\mathbf{R}\_{12})/(1+s\mathbf{C}\_3\mathbf{R}\_9) \tag{11}$$

$$H\_3(s) = \mathcal{R}\_{17} / \left(\mathcal{R}\_{13} + \mathcal{R}\_{15}\right) = \mathcal{R}\_{18} / \left(\mathcal{R}\_{14} + \mathcal{R}\_{16}\right) \tag{12}$$

$$H\_4(s) = 1/(1 + s\mathcal{C}\_5(\mathcal{R}\_{19} + \mathcal{R}\_{20})) \tag{13}$$

The final transfer function can be calculated by substituting the parameters in Table 2 into Equation (9). The result is shown in Figure 10.

**Figure 10.** Overall amplitude-frequency characteristic curve of low-noise amplifier circuit.

The gain of the IF3602 LNA circuit is kept stable at 55 dB in the 100 Hz–100 kHz. Because the PSD of the TEM low-frequency signal is large, if the gain at the full band is maintained stable, the signal will be more likely to saturate in the early stage. In this case, a non-ideal high-pass filter can be used to reduce the gain of the amplifier circuit for low-frequency signals, because the gain of the non-ideal high-pass filter is weak in the low frequency and large in the high frequency. A more accurate TEM secondary field signal can be recovered by adding a transfer function correction during data processing. The noise PSD at the output of the circuit was detected using an Agilent 35670A dynamic signal analyzer when shorted the input under EM shielding conditions. In order to record the noise floor of the amplifier circuit detail, the output noise floor of the IF3602 low-noise amplifier and LT1028 amplifier in the frequency bands of 0–800 Hz, 800–1600 Hz, and 1.6–52.8 kHz were collected and spliced. The equivalent input noise floor of the two is shown in Figure 11.

**Figure 11.** Comparison of the noise floor between the IF3602 circuit and the LT1028.

According to Figure 11, the noise floor of the IF3602 differential amplifier at 100 Hz, 1 kHz, and 10 kHz are 2.15nV/√Hz, 1.12nV/√Hz, and 0.60nV/√Hz respectively, which are lower than the corresponding frequency noise of the LT1028 as follows: 3.50nV/√Hz, 3.04nV/√Hz, and 2.39nV/√Hz. The noise floor of the IF3602 circuit is significantly lower than the noise floor of the LT1028 circuit in the TEM band of 100 Hz–52.8 kHz.

Figure 12 compares the actual noise curve of the IF3602 differential amplifier circuit with the calculated one based on Table 2 and Equation (7). The actual noise is close to the theoretical noise, and both of them reach below 1nV/√Hz above 1 kHz. However, the noise floor is different at low frequencies. The reason is that, when calculating the thermotical noise, only the corresponding noise of the device at 100 Hz given by the datasheet was used. However, the JFET is seriously disturbed by 1/*f* noise at low frequency in practice, and the amplitude of 1/*f* noise is inversely proportional to the frequency. So, in the high-frequency band, the theoretical noise is close to the actual noise, and the actual noise floor deviates from the theory.

**Figure 12.** Comparison of measured noise data and theoretical calculated values of IF3602 low-noise amplifier circuit.
