## 2 Technology and Methods
### The Structure of the Linear Amplifier  
In the process of designing a hybrid power modulator, the output resistance of the linear amplifier should be very low to drive the following circuits. Its high voltage gain ensures tracking accuracy. The wide bandwidth of the linear amplifier is required for quick response. The unit gain bandwidth requires a large loss current while increasing the linear stage bandwidth, and a large current consumption. How to meet the requirements of the linear amplifier is also a key point. The current-mirror amplifier with current reuse is based on a current mirror operational trans-conductance amplifier (OTA) as shown in Figure 4. An additional control circuit is added to increase the output current, as shown in Figure 5. In static conditions, the static currents of M3 and M4 are shunted by adding two transistors M12 and M13, which reduces the output current and indirectly increases the output impedance. The magnitudes of the current flowing through M12 and M13 are controlled by the detection input differential voltage of M10, M11, M14, and M15. The output impedance, gain, and slew rate of a current-mirror amplifier with current reuse are better than those for a current-mirror OTA under the same working conditions. Therefore, this structure of a current-mirror amplifier with current reuse is more suitable for the design of linear amplifiers. Figure 4: Current-mirror amplifier with current reuse. Figure 5: Schematic diagram of phase enhancement method circuit. The stability of a linear amplifier depends primarily on the distribution of poles and zeros. The phase margin (PM) is referred to as a unique parameter for a closed-loop system. A good phase margin can make the system more stable. How to ensure that the linear amplifier has suitable stability is also a key issue in the study of power supply modulator chips. One approach to accomplishing this is to introduce a compensation circuit to move poles into the system to stabilize the whole system. Utilizing traditional Miller compensation [13], the main idea is to reduce the bandwidth in exchange for the improvement of the phase margin. In this paper, a phase enhancement method in the main amplifier is used to improve the stability of the linear amplifier [14,15]. In this paper, two zeros are introduced by using negative feedback and positive feedback resistor-capacitor links. Two zeros are used to cancel the original two poles in the main amplifier, thereby indirectly pushing the frequency of the secondary poles out of the bandwidth range as shown in Figure 6. This increases the bandwidth and phase margin. As the frequency of the zero is entirely determined by the passive component values, zero-pole cancelation can be easily achieved [15]. The second pole (\(P_{2}\)) can be eliminated by adjusting the first zero (\(Z_{1}\)) with the sum of \(R_{1}\) and \(R_{2}\). The second zero (\(Z_{2}\)) can then be tuned to the frequency of the third pole (\(P_{3}\)) [15]. This paper assumes that \(C_{1}\) = \(C_{1}\) = \(C\) [16]. \[Z_{1}\approx-\frac{1}{C(R_{1}+R_{2})} \tag{1}\]  
\[Z_{2}\approx-\frac{R_{1}+R_{2}}{C(R_{1}R_{2})} \tag{2}\]  
\[P_{1}\approx-\frac{1}{(C_{L}+2C)r_{\sigma 4}+2 Cr_{\sigma 3}} \tag{3}\]  
\[P_{2}\approx-\frac{(C_{L}+2C)r_{\sigma 4}+2 Cr_{\sigma 3}}{2C_{L}Cr_{\sigma 4}r_{ \sigma 3}+C^{2}(4r_{\sigma 4}r_{\sigma 3})} \tag{4}\]  
\[P_{3}\approx-\frac{2C_{L}+4C}{C_{L}C(R_{1}+R_{2})} \tag{5}\]  
In order to make full use of the power supply voltage and reduce power consumption, the output stage needs to provide a large current and a small quiescent current. The output stage adopts class-AB amplifier architecture after compromise M53 and M54 are used to form a floating voltage source to fix the gate voltage to make the output stage work in class-AB mode. As for the compensation of the secondary amplifier and the class-AB amplifier, since the pole of the main amplifier is offset by the introduced zero point, the main pole of the secondary amplifier becomes the main pole of the whole circuit.