Synthesizers

Chris Angove has significant design and development experience involving synthesizers, both the fractional N and dual modulus types. He has designed a number of synthesizer components including VCOs, filters, mixers, amplifiers, couplers, attenuators and programming interfaces as well as the compartmentalised PCBs to carry the components. Many of the synthesizers he has worked on were required to meet some tight phase noise specifications, usually over temperature, and much of the development time was devoted to improvements to achieve these. He is also familiar with achieving other requirements such as lock time, spurious emissions, output power level, pushing/pulling, power consumption / efficiency  and frequency stability. Some of the synthesizers have been multi-loop so these have presented additional challenges in essentially making several synthesizers work together effectively.

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CONTENTS

  1. Phase Locked Loops
  2. Second Order Synthesizer Feedback Loop
  3. Synthesizer Parameters

  1. Phase Locked Loops
  2. There are many excellent references I often use for anything connected with phase locked loops (PLLs) for example Robins and Gardner.. In the last 30 years or so, the volume of PLL circuits has exploded (and a few PLL circuits have exploded as well). Synthesisers for a multitude of applications from high stability low phase noise through fast hopping and beyond are widespread in everyday equipment. Cellular or mobile communications, especially digital in the last 10 years or so, have promoted this even more. Synthesizer ICs have progressed from dividers only, through programmable dividers, inclusion of phase detectors, loop filters and even VCOs.

    A PLL is a form of negative feedback, so the theory is totally based on feedback theory. In electronics feedback usually comprises a portion of voltage fed from the output of an amplifier to its input and there are of course various ways of doing that. The simple voltage case would be DC or steady state, that is, considering the conditions after a long time has elapsed. More realistic and practical applications of feedback would include complex variations of voltage with respect to time. A PLL is one example.

    A PLL works at a fixed frequency once steady state has been achieved. A simple example is shown below and would typically be used to provide an appreciable level of sinusoidal signal output, but locked to a high quality, stable, relatively low power or 'reference' signal. A VCO provides appreciable signal, but with little accurate control of frequency or, more precisely, phase. A reference frequency oscillator, such as a crystal source, provides a high quality source but of limited output power. The PLL provides the best of both worlds.

    As we know, the parameter 's' is complex frequency equivalent to jw. Mathematically this is a very useful tool, if only that 's' is less to write than 'jw'. However I think there is more to it than this, Laplace transforms to start with. Laplace transforms may be used to transform from the time to the frequency domain or, in its inverse form, from the frequency to the time domain, similar to Fourier transforms.

    2ndorder3.jpg

    The function of the phase detector is to compare the phase of a fed back sample of the VCO signal with that of the reference frequency oscillator. The phase detector output is an error signal proportional to the difference in phase between these two signals. The error signal is integrated by the loop filter and used to control the VCO frequency in such a direction that it corrects for the phase error. This will reduce to zero when phase lock is achieved.

    We always have 3 varying parameters: phase (f), angular frequency (w) and of course time (t). For a fixed frequency then

    pll_3.gif

    Whenever phase varies, so does the frequency, since the angular frequency is defined as the derivative of phase with respect to time.

    pll_4.gif

    Another way of putting that is

    pll_5.gif

    Although there is a physical electrical connection forming a closed loop, the voltage within that loop is not the only parameter used to control it. Starting at the VCO, a voltage input controls a frequency output or perhaps more accurately a frequency deviation output. The phase detector provides a voltage output from the comparison of the phases of 2 inputs. So we have frequency, phase and voltage. The dimensions of frequency are 1/TIME so we have time as well. All this gets horrendously confusing and I don't pretend to understand it in any great depth.

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  3. The Second Order Synthesizer Transfer Function
  4. This is an extension of the phase locked loop but incorporating a change in frequency. There is a practical limit to the upper frequency at which the phase detector will operate and very often the actual required

    2ndorder2.jpg

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  5. Synthesizer Parameters
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