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Characterizing MSP cells

posted Oct 2, 2015, 3:42 PM by Rohit Sharma   [ updated Oct 2, 2015, 3:43 PM ]
Keywords: level shifter, differential amplifier, ground level 
Category: VLSI characterization 

Introduction: 
Challenges of characterizing digital cells start to look easy in the face of mixed signal cells with parameters that defy assumptions of digital cells. One of the assumption digital cells make is ground voltage is zero, which does not hold good for mixed signal cells like level shifter, differential amplifiers etc. How does delay measurement change with violation of this assumption is the topic of this article.

Below is an example waveform of such a cell.

multi threshold input and output waveforms of differential amplifier
Figure: multi rail wave forms of a differential amplifier 

Note that this cell appears to have differential input-pair and differential output pair. Input pair switch in different direction from zero volt to 0.73 volt, whereas output pair switched from 0.30 volt
to 0.68 volt.
Measuring Arc Delay: 
With changed voltages, one has to come up with new threshold voltages to find delay points. As we discussed in previous blog, delay measurement involves following 8 threshold voltages.
  • slew_low_rise_thr
    • A point close to low supply voltage in a rising voltage waveform used in measuring slope.
  • slew_high_rise_thr
    • A point close to high supply voltage in a rising voltage waveform used in measuring slope.
  • slew_low_fall_thr
    • A point close to low supply voltage in a falling voltage waveform used in measuring slope.
  • slew_high_fall_thr
    • A point close to high supply voltage in a falling voltage waveform used in measuring slope.
  • in_rise_thr
    • A voltage point in a rising voltage waveform at input port used in measuring delay.
  • in_fall_thr
    • A voltage point in a falling voltage waveform at input port used in measuring delay.
  • out_rise_thr
    • A voltage point in a rising voltage waveform at output port used in measuring delay.
  • out_fall_thr
    • A voltage point in a falling voltage waveform at output port used in measuring delay.
With these definition, we find rail swing for both input and output pins as follows:
  • in_rail_swing = pin_high_volt(in) - pin_low_volt(in)
  • out_rail_swing = pin_high_volt(out) - pin_low_volt(out)
Once swing has been determined, one can find input and output voltage levels crossing thresholds as follows:
  • in_volt = pin_low_volt(in) + in_thr*in_rail_swing
  • out_volt = pin_low_volt(out) + out_thr*out_rail_swing
One must substitute in_thr and out_thr definition from threshold table above, depending on the input and output transition. After that, delay of the cell is as simple as following subtraction:
delay = Timeout_volt - Timein_volt
Conclusion: 
In this article, we presented method and equations to compute delays with ground voltages other than zero. One can easily extend this method to find equation to compute output slope with ground voltages other than zero.
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