Phase-Locked Loop: Understanding Coherent Demodulation of AM

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In summary, the PLL system needs to have a feedback transfer function that is different from the original system's feedback transfer function in order to achieve stable operation. The steady state phase error is the value of the phase error at which the PLL system is stable.
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cyeokpeng
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Though I have gone through a communications course in EE, I am still very blur about the Phase-locked loop system in performing coherent demodulation of AM signal.

The problem with direct coherent detection straight from the received AM signal from the receiver antennae is that the local oscillator cannot reproduce the exact same carrier frequency to be hecterodyned with the AM signal to bring it back to baseband. Many reasons colud have caused that, for example, the phenomenon of frequency shifting due to relative motion of the Tx or the Rx (What is the name I forgot), etc etc. So there needs to be a negative feedback to ensure the frequency of the local oscillator approaches the frequency of the carrier in the AM signal. But I really do not understand the mathematics analysis of the system. Can anyone give me an insight to that?
 
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A phase-locked loop generally consists of at least two parts:

1) A voltage-controlled oscillator (VCO). A higher input voltage results in a higher frequency, for example.

2) A phase detector. This device compares the phase of the received carrier and the oscillator's output, and produces an error signal. The error signal is fed back into the VCO to adjust its frequency.

Many PLLs also include a thrid component:

3) Loop filter. This filter generally is designed for a specific application, and prevents ringing, overshoot, and other unwanted behavior. The loop filter keeps the loop stable.

Keep in mind that a constant phase error corresponds to a simple frequency error. If the received carrier has a higher frequency than the VCO, the phase error will be constantly positive, making the VCO oscillate more rapidly. If the received carrier has a lower frequency than the VCO, the phase error will be constantly negative, making the VCO oscillate more slowly.

- Warren
 
  • #3
Mmm, I am a bit clearer now.

Another question, the PLL can be designed to be a first-order PLL or second-order PLL. How do you design such PLL systems such that they have different order transfer function characteristics? I have just learn feedback theory, systems and control course, and I still do not know how to find the transfer function of a system H(s) with a feedback transfer function H1(s).

And what is the meaning of steady state phase error?
My conception of steady-state phase error is the steady state phase error output signal when passed through the PLL system, and since the PLL is designed to be stable (in phase lock), the steady state phase error will be finite, and we can use the final value theorem of Lasplace tranform to work out its steady state phase error value.
Hope I am correct.
 

1. What is a Phase-Locked Loop (PLL)?

A Phase-Locked Loop is an electronic circuit that is used to generate a stable and precise output signal by comparing the phase of an input signal with a reference signal. It is commonly used in communication systems for coherent demodulation of AM signals.

2. How does a PLL work?

A PLL consists of three main components: a phase detector, a loop filter, and a voltage-controlled oscillator (VCO). The phase detector compares the phase of the input signal with the reference signal and produces a control voltage for the VCO. The loop filter smooths out the control voltage and the VCO uses it to generate an output signal with the same frequency and phase as the reference signal.

3. What is the purpose of using a PLL for AM demodulation?

The main purpose of using a PLL for AM demodulation is to recover the original modulating signal from the modulated carrier signal. This is achieved by using the reference signal as a carrier and comparing its phase with the input signal. The output of the PLL will then be a demodulated signal that can be further processed for signal extraction.

4. What are the advantages of using a PLL for AM demodulation?

One of the main advantages of using a PLL for AM demodulation is its ability to accurately recover the modulating signal even in the presence of noise and interference. It also provides a stable and precise output signal, making it suitable for communication systems that require high accuracy and reliability.

5. Are there any limitations of using a PLL for AM demodulation?

While PLLs are generally reliable, there are some limitations to using them for AM demodulation. One limitation is that they require a stable and accurate reference signal to function properly. Additionally, they may introduce some phase noise and distortions in the output signal. However, these limitations can be minimized with proper design and implementation.

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