# Physical Simulation-Based Calibration for Quantitative Real-Time PCR
## 2 Principle and Structure  
### Principles of Calibration Device  
The principle diagram of the developed calibration device is shown in Figure 1. The temperature acquisition module employs a high-precision thermistor encapsulated within a purple copper casing. The fluorescence output module utilizes calibrated light-emitting diodes (LEDs) as standard light sources that are traceable to a spectrometer, encapsulated with polytetrafluoroethylene (PTFE) for optical transparency. These two components are nested together to form a calibration unit, that is, a probe. The outer contour of probes is designed to fit snugly into the inner contour of the porous metal block of qPCR instruments, ensuring an effective fit and accuracy in temperature data collection. In the device host, the selected ADC for the calibration device features low noise (40 nVrms) and low power consumption (400 uA), along with a relatively high sampling  
Figure 1: Schematic diagram of calibration device. rate. The acquisition module is constructed to connect two sets of ADCs and one set of channel switches. Each set interfaces with four temperature probes, with each probe acquiring data four times to calculate an average value. This allows the calibration device to filter out noise and other similar interferences. Probes numbered 1 to 8 undergo cyclic serial acquisition, facilitating the output of two measurements per second. To enable wireless control and data transmission with computer software, the device employs 2.4 GHz low-power Bluetooth technology as the communication protocol. The ideal PCR reaction amplification curve should satisfy Equation (1). However, actual PCR reactions are non-ideal and are influenced by various factors such as primers, enzymes, etc., conforming to the description in Equation (2) [20]. \[X_{n}=X_{0}\times 2^{n} \tag{1}\]  
\[X_{n}=X_{0}\times(1+E_{n})^{n} \tag{2}\]  
\(X_{n}\) represents the amount of amplified product after the nth cycle; \(X_{0}\) denotes the initial template quantity; \(E_{n}\) signifies the amplification efficiency; and \(n\) indicates the number of amplification cycles. According to Equation (2), in actual PCR reactions, a typical amplification process follows an S-shaped curve, including the background phase, exponential amplification phase, and plateau phase. Based on this theory, the calibration device can control the standard light source within the probe based on temperature changes collected by the temperature acquisition module. This control ensures that the light emission intensity changes according to a predefined process, simulating the brightness changes of fluorescence groups during the amplification reaction. The simulated fluorescence is received by the qPCR instrument to mimic a typical amplification curve. The controller of the calibration device drives different electric current levels to the fluorescence output module of probes, resulting in varying intensities of fluorescence brightness. Specifically, during the initial stage, it simulates the background phase by causing only minimal changes in standard light source emission, resulting in growth below a certain threshold. In the second stage, it simulates the exponential amplification phase by causing a fluorescent brightness change that follows an exponential pattern after subtracting background noise. And, during the beginning of this phase, it simulates the pre-set Ct value. This means that when the number of cycles corresponding to this Ct value is reached, the standard light source's emission undergoes a slight increase just enough to surpass the threshold and be detected by the qPCR instrument. In the third stage, it simulates the plateau phase where standard light source emission gradually reaches 100%. After completing simulation of an S-shaped curve representing amplification, the probe can also be designed to simulate the melting curve process by emulating half DNA denaturation-induced fluorescence and reducing standard light source emission by equal magnitude.