Zola 2023-03-19T00:00:00+00:00 https://mletemple.fr/en/tags/analogue-electronics/atom.xml 2023-03-19T00:00:00+00:00 2023-03-19T00:00:00+00:00 Maxime Letemple https://mletemple.fr/en/blog/pll/ <p>A PLL is an electronic circuit that can be used to generate an output signal that is synchronized in frequency and phase with an input signal. The main function of a PLL is to track and synchronize the frequency and phase of a reference signal with an output signal.</p> <figure> <img class="transparent no-hover"alt="Analog phase locked loop"src="pll.svg"/> <figcaption>Analog phase locked loop</figcaption> </figure> <h1 id="phase-detector">Phase Detector</h1> <p>The phase detector receives in input two signals $v1(t)$ and $v2(t)$ and returns a signal $v(t)=K_d.f(\Phi_{ref}-\Phi_{osc})$.</p> <p>Usual phase detectors are the Balanced Mixer(for sinusoid signals) or XOR comparator(for digital signals).</p> <h1 id="low-pass-filter">Low-pass filter</h1> <p>The main objective of the low-pass filter is to generate the voltage used for the VCO. Usually, the transfer function is $F(p)=\frac{1}{1+\tau P}$ with $\tau = RC$ for a RC filter.</p> <h1 id="vco">VCO</h1> <p>The VCO aims to generate the output signal. The output signal is linear around its working pulsation. Indeed, $\omega_{VCO} = \omega_{1} + K_0(U_{VCO} - U_1)$, with $K_0$ the gain of the VCO.</p> <hr /> <h1 id="extension-for-frequency-synthesizers">Extension for frequency synthesizers</h1> <p>In order to synthesize higher frequencies, a frequency divider can be added on the feedback branch. By this way, $f_{VCO}=N.f_{ref}$. $f_{ref}$ is the reference signal, is is called step of synthesis. Indeed, for $N = N+1$. $f_{VCO}=N.f_{ref} + f_{ref}$</p> <hr /> <h1 id="reminder">Reminder</h1> <p>Useful functions and values:</p> <p>Transfert function of a linearized PLL without divider:</p> <p>$$H(p)=\frac{K_d K_0 F(p)}{p + K_d K_0 F(p)} = \frac{\omega _n ²}{\omega _n ² + 2\xi \omega _n p + p²}$$</p> <p>$$\omega _n = \sqrt{\frac{K_0 K_d}{\tau}} \ \xi = \frac{1}{2} \frac{\omega _n}{K_0 K_d}$$</p>