Using VCO to achieve direct frequency modulation of varactor diode 2

The principle of direct frequency modulation of varactor diode - the diode can change the width of the space charge region by changing the applied reverse voltage, thereby changing the size of the potential barrier capacitance. Varactor diode is a special pn junction diode made using this characteristic. It is a nonlinear circuit element with variable reactance, and is generally made of silicon or gallium arsenide. Figure 1 is the characteristic curve of a varactor diode, and Figure 2 is a schematic diagram of direct frequency modulation of the varactor diode. ---When a varactor diode is reverse biased, the junction capacitance can be represented by the following equation:, where vd is the built-in potential difference of the pn junction, cj0 is the junction capacitance when the applied reverse voltage u=0, and n is the capacitance change index. The n value depends on the impurity distribution pattern of the pn junction of the varactor diode. For a gradual transition junction, the n value is equal to 1/3, for a abrupt transition junction, the n value is equal to 1/2, and for a super abrupt transition junction, the n value is between 1 and 5. ---Varactor diode  cannot operate in the forward bias region in reverse biased direct frequency modulation circuits. As shown in Figure 2, in order to ensure that the varactor diode maintains a reverse bias during the modulation voltage change process, a reverse DC bias e0 greater than the amplitude of the modulation signal must be added. Therefore, in single tone modulation, the voltage u on the varactor diode is equal to e0+u ω cos ω t, and the change law of the junction capacitance is obtained (see this issue of the magazine) - in the equation, it is called the capacitance modulation degree, which is the junction capacitance at the static operating point. ---The resonant angular frequency of the oscillation circuit is: (see this issue of the magazine) - In the equation, is the oscillation angular frequency without modulation, that is,diode  the carrier angular frequency. Using the equation as a variable and expanding it into a Taylor series at, we obtain: (see this issue of the magazine) - From the above equation, it can be seen that the frequency variation of the oscillator not only contains components proportional to the modulation signal, but also includes the second harmonic and higher harmonic components of the modulation signal, as well as the drift of the center frequency. Generally, under the premise of ensuring the maximum angular frequency deviation, tubes with a larger capacitance index n are selected to reduce the capacitance modulation degree m, thereby reducing the drift of the center frequency, improving the frequency stability of the oscillator, and eliminating various harmonic distortion components to achieve linear frequency modulation diode