RC Circuit Analysis and Design The RC circuits in Figure P10–67 represent the situation at the input to an oscilloscope. The parallel combination of R1 and C1 represent the probe used to connect the oscilloscope to a test point. The parallel combination of R2 and C2 represent the input impedance of the oscilloscope.

(a) Assuming zero initial conditions, transform the circuit into the s-domain and find the relationship between the test point voltage VS(s) and the voltage VO(s) at the oscilloscope’s input.

(b) For R2 ¼ 15MV and C2 ¼ 3 pF, determine the values of R1 and C1 that make the input voltage a scaled duplicate of the test point voltage.

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ww Test point R1 + -o + vo(t) vs(t) C1 R2 C Probe FIGURE P10-67 O'scope