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Open loop gain and open loop phase for an oscillator

Pictou

 Hello,

I'm designing an oscillator with a quartz (Pierce model). The circuit is basically an amplifier and the quartz. I would like to measure the open loop gain and phase however I'm not sure about the method.

 First method I tried is the following :

I disconnected the loop at the gate of the MOS amplifier inverter. Put a vac source and set the AC amplitude to 1V.I copied the schematic of  the amplifier and pasted it at the output of the crystal, this way the crystal will see the same load as if it was in closed-loop. Then I measure the gain at the output of the crystal using a HB analysis.

 

Second method is :

I used the middlebrook analysis, which is stb in cadence. However I'm skeptical about this method as stb is to check the stability of the system. And, as I'm using an oscillator, I'm not supposed to be stable. However I'm still measuring an open loop gain and phase with stb analysis.

 

My question is which method is correct? I really have no idea on how to answer that question, so I'm here.

 

Thank you.

Parents

  •  This technique is independent of Cadence and can be used with any circuit simulator or circuit analysis.

    Your concept is correct. I would recommend placing the C0 of the quartz model and the parasitics on each pad in your oscillator amplifier. In other words, place the current source across the two the input terminals of the oscillating amplifier where the two terminals of the quartz crystal unit are normally placed. Remove the quartz crystal unit mode, but include the C0 of the resonator and any parasitics on either side of the quartz crystal unit (due to board, pads, etc). Assuming the DC operating point forces the oscillating amplifier into its high gain region, the real part of the resulting voltage response using an AC value of 1 A in the current source will illustrate the "negative resistance" charactersitic of the oscillating amplifier as a function of frequency. The imaginary part provides an estimate of the reactance of the oscillating amplifier. From the real part, and knowing the range of quartz crystal unit series resistance, by inspection you can tell if sufficient gain exists to support oscillation. The gain is the absolute value of the negative resistance over the quartz crystal unit's series resistance. If there were no non-linear effects, which is not the case as the oscillator relies on those to limit the amplitude of oscillation, the exact frequency of oscillation could be determined by solving the equation Xamp + Xresonator = 0 where Xamp is the reactance of the oscillating amplifier and Xresonator is the sum of the Ls and Cs reactances of the quartz crystal unit.

     

    I hope this helps.

    Shawn

Reply

  •  This technique is independent of Cadence and can be used with any circuit simulator or circuit analysis.

    Your concept is correct. I would recommend placing the C0 of the quartz model and the parasitics on each pad in your oscillator amplifier. In other words, place the current source across the two the input terminals of the oscillating amplifier where the two terminals of the quartz crystal unit are normally placed. Remove the quartz crystal unit mode, but include the C0 of the resonator and any parasitics on either side of the quartz crystal unit (due to board, pads, etc). Assuming the DC operating point forces the oscillating amplifier into its high gain region, the real part of the resulting voltage response using an AC value of 1 A in the current source will illustrate the "negative resistance" charactersitic of the oscillating amplifier as a function of frequency. The imaginary part provides an estimate of the reactance of the oscillating amplifier. From the real part, and knowing the range of quartz crystal unit series resistance, by inspection you can tell if sufficient gain exists to support oscillation. The gain is the absolute value of the negative resistance over the quartz crystal unit's series resistance. If there were no non-linear effects, which is not the case as the oscillator relies on those to limit the amplitude of oscillation, the exact frequency of oscillation could be determined by solving the equation Xamp + Xresonator = 0 where Xamp is the reactance of the oscillating amplifier and Xresonator is the sum of the Ls and Cs reactances of the quartz crystal unit.

     

    I hope this helps.

    Shawn

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