学PLL求助

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Two recommended structures for the VCO

Two recommended structures for the VCO.


对PLL不熟，初学，请问哪本书里或者哪些论文、在线博客里有上边图中这个原理的推导过程吗？谢谢

bill66656

问过AI, 图1里这三个相位信号有什么区别，图2里的传输函数对应了哪一种作为输入信号的VCO？解答如下


In the first figure, the three phase signals represent different ways that phase can vary with time:

1. **θ₁(t) = ΔΦ·u(t)**:
   - This is phase modulation where the phase shift is proportional to the input signal u(t). The phase changes instantaneously with the input signal.

2. **θ₁(t) = Δω·t**:
   - This represents a linearly increasing phase due to a constant frequency offset Δω. The phase accumulates linearly over time.

3. **θ₁(t) with ω₁(t) = ω₀' + Δω·t**:
   - Here, the frequency itself is changing linearly over time, leading to a quadratic increase in phase. This is a case of a frequency sweep or chirp signal.

In the second figure, the transfer functions of the two VCO structures can be analyzed as follows:

- **Figure (a)**: The transfer function from Δω₀ to y is a cosine function. This corresponds to a VCO where the output is a cosine wave with a phase that can be modulated. The phase is determined by the integral of the frequency deviation over time. If the input is a constant frequency deviation Δω, then the phase would accumulate linearly as in the second case (θ₁(t) = Δω·t).

- **Figure (b)**: The transfer function also involves a sine function with a negative sign. This structure is similar to (a) but uses sine functions with a phase shift, which could be part of a quadrature oscillator setup.

Both structures in the second figure are examples of VCOs that can generate signals with phases that vary according to the input frequency deviation. The first case in the first figure (θ₁(t) = ΔΦ·u(t)) would correspond to a VCO where the phase is directly modulated by the input signal, which could be the case if u(t) represents the frequency deviation input to the VCO. The second case (θ₁(t) = Δω·t) corresponds to a situation where the VCO has a constant frequency offset from the nominal frequency ωₙ, leading to a linearly increasing phase. The third case involves a time-varying frequency, which would result in a more complex phase behavior not directly shown in the second figure's transfer functions. The second figure's transfer functions are more aligned with the second case (θ₁(t) = Δω·t) when considering a constant frequency deviation input.