## 4 Analog Circuit  
### Circuit Design  
In detecting wire rope, the MFL signal collected by the sensors is tiny, but the intensity of the magnetic field decreases exponentially as the lift-off distance linearly increases. Aiming to amplify the weak signal and remove noise signal, a signal processing circuit to perform accurate filtering was proposed in this section. Considering the application background of steel wire rope is mostly mine and ocean, where the working conditions are harsh, some fundamental requirements have been proposed, including the following:  
* High input impedance; Signal source internal resistance can reach 100 \(\Omega\). If the loss on the signal source is required to be less than 1%, then the input impedance is required to be more than 10 k\(\Omega\). * High voltage gain;  
Figure 17: The output voltage of three types of coil arrays. Figure 18: Coil structure parameters. The signal collected is feeble at the considerable lift-off detection distance (>30 mm), even less than millivolts. Therefore, the circuit amplification gain should reach more than 1000 times. * Single power supply;  
Due to the dual power supply with the negative voltage supply, additional voltage converter and coupling capacitors are required, leading to the complex design of the circuit and more noise sources. To simplify the structure of the circuit and reduce the size of the signal processing module, a single power supply has been adopted, which is also convenient to install and arrange. * Low noise;  
Owing to the harsh environment with many kinds of noise, electronic components must have high stability to avoid interference from various noises. Besides, parameter characteristics of components do not change significantly with temperature. * Proper bandwidth;  
According to many experiments, the frequency range of the damage signal of the wire rope under normal speed conditions is below 200 Hz. Even though the wire rope is running at a higher speed, the frequency range of the defects signal is still less than 500 Hz. As a consequence, amplification of low-frequency signals will be the focus. According to the targets above, the circuit structure is divided into three functional modules. The first one is weak signal amplification. The second one is a low pass filter. The third one is the high pass filter. The operational amplifier circuit is composed of OPA2188, shown in Figure 19. OPA2188 was chosen from National Instrument as an operational amplifier, and its main features include low drift voltage, low noise, zero drift, and high CMR. Its pin diagram is shown in Figure 20 In means input and out means output. It is a dual operational amplifier. V means DC voltage. Figure 19: Operational amplifier composed of OPA2188. Figure 20: OPA2188 pin diagram. When designing the operational amplifier, a two-stage amplification layout was adopted. The amplification factor \(A_{1}\) of the first-stage non-inverting amplifier circuit is  
\[A_{1} =1+\frac{R_{3}}{R_{1}} \tag{1}\]  
\(R_{1}\) is the balance resistor in the first-stage amplifier circuit, and it is used to provide a DC path to the non-inverting input. \(R_{2}\) forms a loop with GND to generate base current. The amplification factor \(A_{2}\) of the second-stage inverting amplifier circuit is  
\[A_{2} =-\frac{R_{6}}{R_{4}} \tag{2}\]  
Amplification of every stage was set to 100, so the overall amplification is 10,000. \(R_{5}\) is the balance resistor in the second-stage inverting amplifier, and it is used to provide suitable static bias and eliminate the effect of base current on the output voltage. Meanwhile, the operational amplifier was supplied by a DC bias voltage of 2.5 V while using a single power supply. Considering the signal collected is altering voltage, the output voltage swing around 2.5 V. On the one hand, the negative voltage collected can be output correctly. On the other hand, a more excellent dynamic range can be achieved.