*3.1. Selection of LNA Circuit Components*

Because of the characteristics of the wideband and large dynamic range of the TEM signal, the suitable amplifier must have a sufficient gain-bandwidth product, as mentioned, and a low-noise cascade amplifier circuit needs to be designed to achieve reliable signal amplification. The Frith formula, shown in Equation (1), reflects the relationship between the overall noise of the cascaded circuit and the noise of the circuits at all levels as follows:

$$F = F\_1 + \frac{F\_2 - 1}{K\_1} + \frac{F\_3 - 1}{K\_1 K\_2} + \dots + \frac{F\_M - 1}{K\_1 K\_2 \cdot \dots \cdot K\_{M-1}} \quad (M = 2, 3, \dots) \tag{1}$$

*F* is the total noise figure of the cascaded amplifier, *FM* is the noise figure of the *M* amplifier, and *KM*−<sup>1</sup> is the gain of the *M*−1 amplifier. The noise of the cascaded amplifier is mainly restricted by the first-stage amplifier, and the influence of the latter stage is slighter, which means reducing the noise floor of the first-stage amplifier is the primary consideration when designing a low-noise system for weak signal detection.

To optimize the noise floor of the first-stage amplifier circuit, a low-noise device must be selected as the core of the circuit. Common choices of low-noise devices are bipolar transistors (BJTs), JFETs, and IOAs. Because BJT devices and BJT-type IOAs have a low noise floor in low-frequency and mid-frequency bands, they are generally used to make TEM preamplifiers, but with the development of low-noise JFET, such as LSK389B and 2SK3320. These components significantly reduce device voltage noise when their own current noise is negligible. These give low-noise JFETs the advantage of a low device noise floor and simple noise components, which are more suitable for making LNAs. In order to select the low-noise device for the preamplifier, we compared the noise performance of common low-noise devices, and the results are shown in Table 1.


**Table 1.** Comparison of noise performance of low-noise devices.

Table 1 shows that IF3602 has very low voltage noise (0.5nV/√Hz@100Hz) and the noise frequency is only 100 Hz. The principle of a JFET is using the electric field effect in the semiconductor to change the barrier width of the gate PN junction by controlling the gate-source voltage VGS and using the pinch-off of the depletion layer to control the internal carriers. No current flows between the gate and the source, so the current noise is negligible. This feature simplifies the noise model of the JFET amplifier circuit. According to the comparison, we proposed a low-noise differential circuit design for the JFET IF3602 and combined the noise model to optimize the external circuit.

#### *3.2. Overall Design of Low-Noise JFET Amplifier Circuit*

Based on the characteristics of the TEM signal analyzed in Figures 2 and 3, we designed the amplifier circuit shown in Figure 4. According to the functions of each cascade amplifier, the LNA circuit is divided into a four-level structure, as shown in Figure 5. The first-stage circuit is a differential circuit based on the JFET IF3602, which can achieve low-noise and high-gain amplification for the received signal. The low noise floor of the amplifier circuit means that the impact of circuit noise on the signal-to-noise ratio (SNR) of the TEM signal is weak. Besides, the high gain in the first-stage circuit weakens the impact of the noise

floor in the post-stage circuits. For the differential circuit, it also has the characteristics of high differential mode magnification and low common mode magnification, which can effectively suppress the interference of common mode noise and enhance the antiinterference ability of the TEM device.

**Figure 4.** Schematic diagram of low-noise amplifier circuit.

**Figure 5.** Schematic diagram of the function of the low-noise amplifier circuit.

The second-stage circuit is an amplifier made from the low-noise IOA LT1028 with a high-pass filtering function. Although the noise floor of the LT1028 IOA is not as good as IF3602, its equivalent voltage noise is only 0.85nV/√Hz, and the IOA circuit is easy to design because of its simple structure. Therefore, it is very suitable to be the secondary amplifier. In addition, as shown in Figure 3, it is necessary to reduce the impact of a low-frequency component of TEM to avoid the early signal saturation. Therefore, adding high-pass filtering can make full use of its amplitude-frequency characteristics, to reduce the amplification factor of low-frequency components, and avoid early signal saturation.

The third-stage circuit contains a precision differential amplifier INA105, which integrates a laser-corrected 25 kΩ precision resistor to ensure the gain accuracy of the internal feedback amplifier circuit and reduce the impact of resistance temperature drift on the accuracy of the differential amplifier.

An RC low-pass filter network is used in the fourth stage with a 257 kHz cut-off frequency, which includes the ideal signal frequency band in forwarding modeling, to avoid the influence of high-frequency noise on the circuit and ensure the quality of TEM signals.
