Switching frequency for voltage output in a two-system RC circuit

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Homework Statement


Problem and Diagram stated below
System 2 Input Impedance: 1k ohms
System 1 Output Impedance: 100 ohms
High interpreted as Voltage greater than 2V
Low Interpreted as Voltage less than 0.5V

Circuit schematic of a T-shaped transmission line between System 1 (switch SW1, 5 V source, Rout 10 ohm) and System 2 (R1 100 ohm, C1 10 uF shunt, R2 100 ohm, Rin 1 kohm), with the problem text above it.


Homework Equations


Capacitor Charging eqn:
V=Vo(1-e^-t/RC)

Capacitor Discharging eqn:
V=Voe^-t/RC

f=1/T

The Attempt at a Solution


Posted Below

Handwritten circuit analysis notes: a two-system RC circuit with a Thevenin equivalent sketch, Vin = (Rin/(Rin+Rout)) Vc(t), conditions Vin > 2 and Vin < 0.5, capacitor charge and discharge equations, and time constants of 0.055 s with switch closed and 0.0555 s with switch open.


Handwritten solution on lined paper: charging voltage Vc(t) = 5(1 - e^(-t/1000)) reaching 2.3V, discharge to 0.54V, a sketched Vc(t) against t graph with marked times 7.1x10^-4 s and 0.0159 s, and switching frequency f = 1/T = 60 Hz.

Hey guys. This was a problem given to us on one of our assignments and that was my suggested solution...was wondering if what I did was correct.

Thanks in advance :D
 
Attachments
  • Circuit schematic of a T-model transmission line between System 1 and System 2: SW1 with Vs 5V and Rout 10 ohms, R1 100 ohms, C1 10 µF to ground, R2 100 ohms, and Rin 1 kohm.
    switchingfreq.png
    95.8 KB · Views: 520
  • Handwritten worked solution on lined paper for an RC circuit with two systems: circuit diagrams with resistors and a capacitor, Vin = (Rin/(Rout+Rin)) Vs(t), inequalities giving Vs(t) > 2.2 V and Vs(t) < 1/20 V, and charge/discharge time constants of 1/100 s with a 0.0555 s switching period.
    Scan0009.jpg
    21 KB · Views: 457
  • Handwritten worked solution on lined paper: charging and discharging capacitor equations with numeric steps, a sketched Vc(t) curve rising then falling between two threshold levels, and a final frequency calculation F = 1/T = 60 Hz.
    Scan0010.jpg
    13.5 KB · Views: 471
Last edited:

Discussion

Long story ! Some comments:

First thing that comes to mind for me is the ##\tau## : you sure it's from the 100 Ω only and not the 110 Ω ? (test: let Rin = 1M Ω !)

Second: no need for the ##\approx.## sign. Everything is given 'exactly'. Idem for increasing the 2 * 11/10 to 2.3 and decreasing the 0.5 * 11/10

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As BvU points out, you need to take a closer look at how you determine ##\tau##. Suggestion: find the Thevenin equivalent that the capacitor sees. Note that this will include the load-side resistors too!
 
Good thing gn is on the lookout ! I had forgotten those load side guys. Rustiness...