Why is the frequency different for circuits with the same RC?

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Homework Statement


Circuit schematic of a current source inverter with thyristors T1 to T4 and diodes D1 to D4, a 10 A current source, a 10 ohm resistor, and two 0.1 µF capacitors.


Solution in Book#1
Typed solution text: two capacitors in parallel with Ceq = 0.2 µF, time constant τ = 10 × 0.2 = 2 µsec, full period 4 µsec, frequency = 1/(4 µsec) = 250 KHz.

Solution in Google:
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Handwritten-style worked solution of a switching circuit: series RC network of two 0.1 µF capacitors and a 10 Ω resistor, time constant τ = RC = 4 × 0.5 = 2 µsec, frequency f = 1/τ = 500 kHz.



2. Homework Equations

I don't know which solution is correct. I am struggling to remember this formula.

The Attempt at a Solution


This was a solved example so I didn't attempt.
 
Attachments
  • Voltage commutation circuit with a 100 V source, two 50 ohm resistors, a capacitor C, and two SCRs labelled Th1 and Th2 in a bridge arrangement, with the solution T = RC ln 2 leading to C = 2.88 µF.
    upload_2018-1-26_16-18-44.png
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  • Circuit schematic of a CSI feeding a resistive load, with thyristors T1 to T4 and D1 to D4, two 0.2 µF capacitors, a 5 Ω resistor and a 5 A current source, followed by answer options (A) 1.386 µs, (B) 0.693 µs, (C) 2.8 µs, (D) 0.347 µs.
    upload_2018-1-26_16-48-44.png
    5.3 KB · Views: 581
  • Circuit schematic of a current source inverter with thyristors T1 to T4 and diodes D1 to D4, a 10 A current source, a 10 ohm resistor, and two 0.1 µF capacitors.
    upload_2018-1-26_16-58-22.png
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  • Handwritten-style worked solution with two capacitors in parallel: Ceq = C1 + C2 = 0.2 µF, tau = R Ceq = 10 × 0.2 = 2 µsec, full period 2 × 2 = 4 µsec, frequency = 1/(4 µsec) = 250 kHz.
    upload_2018-1-26_16-58-48.png
    5.2 KB · Views: 570
  • Handwritten solution: Option (C) is correct, then circuit timing notes, two capacitor-resistor series circuits with 0.1 μF, 10 Ω and 0.1 μF, and time constant τ = RC = 4 × 0.5 = 2 μsec and frequency f = 1/τ = 1/(2 × 10⁻⁶) = 500 kHz.
    upload_2018-1-26_16-59-32.png
    13.3 KB · Views: 572
  • Handwritten-style worked solution of a switching circuit: series RC network of two 0.1 µF capacitors and a 10 Ω resistor, time constant τ = RC = 4 × 0.5 = 2 µsec, frequency f = 1/τ = 500 kHz.
    upload_2018-1-26_17-1-13.png
    13.3 KB · Views: 816
  • Typed solution text: two capacitors in parallel with Ceq = 0.2 µF, time constant τ = 10 × 0.2 = 2 µsec, full period 4 µsec, frequency = 1/(4 µsec) = 250 KHz.
    upload_2018-1-26_17-1-24.png
    5.5 KB · Views: 810
Last edited:
It will depend on what load current or voltage is deemed to signal the end of each half cycle.
Capacitors total = 0.2uF.
H bridge current is fixed at 10A. Load = 10 ohm.
Maximum Vload = R * I = 100V.
H-bridge voltage alternates between –100 and +100, so each transition must reverse cap voltage by 200V.

Ignoring the load current and using all the current to charge and discharge the capacitors.
C = Q / V; C = I * t / V; t = C * V / I; t = 0u2F * 200V / 10A = 4u0 sec per transition.
One cycle will take 2 * 4u0 = 8u0 sec = 125kHz.
 
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I guess the In2 formula is for circuit turn off time and not for max frequency. Thanks.
 
Those capacitors are expensive when it comes to current at high switching frequencies.

It appears that this circuit would be more applicable to situations switching at power line frequencies of 50 or 60Hz, than at many tens or even hundreds of kHz. For higher frequencies, this circuit has higher currents charging and discharging the capacitors than it does through the load. After a transition, peak capacitor current can be twice the maximum load current. Total is always 10 amp but the capacitors partly discharge through the load.

Here is an idealised switching circuit simulated by LTspice. Shown clocked at 125kHz (T=8usec), and at 50kHz (T=20usec).
The three traces show total capacitor current, load current and the constant current source.

Driven at 125kHz = 8usec cycle.
LTspice simulation of an H-bridge with a 10A current source, two 0.1µF capacitors and a 10 ohm load; below, a waveform plot of I(C1)+I(C2), I(R1) and I(I1) from 0 to 16µs.


Driven at 50 kHz = 20usec cycle.
LTspice H-bridge schematic with a 10A current source, four SCR switches S1 to S4, diodes D1 to D4, capacitors C1 and C2 at 0.1 µF, and resistor R1 at 10 ohms, above a plot of I(C1)+I(C2), I(R1) and I(I1) against time from 0 to 36 µs.
 
Attachments
  • LTspice simulation of an H-bridge with a 10A current source, two 0.1µF capacitors and a 10 ohm load; below, a waveform plot of I(C1)+I(C2), I(R1) and I(I1) from 0 to 16µs.
    Ideal_8usec.png
    35.7 KB · Views: 392
  • LTspice H-bridge schematic with a 10A current source, four SCR switches S1 to S4, diodes D1 to D4, capacitors C1 and C2 at 0.1 µF, and resistor R1 at 10 ohms, above a plot of I(C1)+I(C2), I(R1) and I(I1) against time from 0 to 36 µs.
    ideal_20usec.png
    36 KB · Views: 394
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Both circuits have same RC. So why is frequency different if we use your first formula in post2?