SLiCAP exercise probe circuit

date: 2010-01-02, author(s): anton, category: SLiCAP_exercise, tag(s): Exercise Probe_circuit SLiCAP.

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Abstract

Oscilloscope probe calibration: poles and zeros, step response and frequency transfer. Theory: “Structured Electronic Design” ISBN 97890-6562-4277. Chapter 18: Network Theory (selected topics).

Contents

Exercise

The figure below shows a photo of an oscilloscope probe and an equivalent network of such a probe.

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The capacitor C2 models the cable capacitance \(C_c=80pF\). The resistance \(R_{se}\) of R1, together with the input resistance of the oscilloscope defines the attenuation of the probe. The compensation capacitor C1 with a capacitance \(C_{cmp}\) should be tuned such that the high-frequency attenuation equals the DC attenuation.

The probe should have an attenuation factor of 10 when it is used with oscilloscopes with an input resistance of \(1M\Omega\) and an input capacitance between \(15pF\) and \(50pF\). The probe will be calibrated with the aid of a voltage source with a source resistance of \(50\Omega\) that provides a square wave calibration voltage with a period of \(1ms\).

  1. Design the value of \(R_{se}\) and the tuning range of \(C_{cmp}\).
  2. Check your result with SLiCAP:
    1. Draw schematic of the probe connected to the calibration source and the oscilloscope; use LT spice and SLiCAP symbols. If you want to set the resistance of the calibration source to zero, use the symbol ‘SLR_r’ for it.
    2. How many poles and zeros does the transfer of the calibration circuit have? Motivate your answer!
    3. How many poles and zeros does the transfer of the calibration circuit have in the case in which the resistance of the calibration source equals zero? Motivate your answer!
    4. Create a SLiCAP project
    5. Create s script file with instructions that:
      1. Print the circuit data on a web page
      2. Determine the transfer function and display it symbolically on a web page
      3. Design the components for proper operation
      4. Estimate the location of the pole(s) and the zero(s)
      5. Print the DC gain and the poles and the zeros of the gain on a web page
      6. Plot the unit step response and display it on a web page
      7. Plot the magnitude and the phase characteristic and display it on a web page
      8. What is the -3dB bandwidth of the complete calibration system?

Exercise

Continuation of the exercise of the previous tutorial.

Assume an oscilloscope with an input capacitance of \(25pF\).

  1. Plot the pole positions as a function of the compensation capacitance.
  2. Plot the magnitude and phase characteristic of the calibrated probe and for the maximum and minimum value of the compensation capacitance.
  3. The influence of a finite area of the current loop formed by the probe tip and the ground lead can be modeled with the aid of an inductance in series with the loop. If the ground clip is not connected, this inductance may limit the bandwidth of the probe.
    1. Study the influence of this ground loop by placing an inductance in series with probe tip with a value between \(10nH\) and \(100nH\).
    2. Use a root-locus plot, a step response and magnitude and phase characteristics.

Please do the exercise yourself before you download the results (latest SLiCAP version only).