need help with RC circuit

[roozbehsf]

Hi all
I have a simple RC ciruit which there is a switch between the resistor and the DC source. Resistor and cap are in series. I wanted to calculate the worst case of the opening and closing time intervals for the switch (assuming the switch can be open and close simultaneously). Can anyone help me with that?

Voltage source = 420 volts
Resistor = 25 ohm, 50W
Cap = 1000uF

 

[duffy]

Sounds like you are asking about the voltages as the RC time constant "t" approaches infinity and zero. (hint)

 

[MrAl]

Hi all
I have a simple RC ciruit which there is a switch between the resistor and the DC source. Resistor and cap are in series. I wanted to calculate the worst case of the opening and closing time intervals for the switch (assuming the switch can be open and close simultaneously). Can anyone help me with that?

Voltage source = 420 volts
Resistor = 25 ohm, 50W
Cap = 1000uF

Hi,

You can not open and close a switch simultaneously. Either it is open or it is closed. There is switch bounce though.

What you need to clarify here is what are you thinking of finding the worst case for? Is it power in the resistor?
If you have a switch and a resistor and a capacitor and a voltage source all in series and you close the switch the cap starts to charge. It takes about five times the RC time constant (which is R times C) to charge up to the full voltage level. Once it is charged, it will stay charged for a while. How long it stays charged (after the switch is opened) depends on the leakage of the cap if there is no bleeder resistor.

So it would help to clarify what you are trying to do.

 

[Gaa]

As already mentioned the cap starts to charge.

Uc(t) = U * [ 1 - e^( -t/T ) ]

where T is the time contant of the RC 'system'.

T = R*C

You can calculate how much time required to reach a given voltage level.

 

[roozbehsf]

Hi,

You can not open and close a switch simultaneously. Either it is open or it is closed. There is switch bounce though.

What you need to clarify here is what are you thinking of finding the worst case for? Is it power in the resistor?
If you have a switch and a resistor and a capacitor and a voltage source all in series and you close the switch the cap starts to charge. It takes about five times the RC time constant (which is R times C) to charge up to the full voltage level. Once it is charged, it will stay charged for a while. How long it stays charged (after the switch is opened) depends on the leakage of the cap if there is no bleeder resistor.

So it would help to clarify what you are trying to do.

Absolutely!
Actually there is another resistor with the value of 1.8kohm in parallel with the cap. Then when the switch opens the cap will be discharge through that resistor.
I want to know for how long that the switch is closed then the switch should be open that the resistor can be cool down and not burn out. In other words I want to know under which condition the resistor will burns out and prevent that situation using an ECU(Electronic Control Unit). Think about short times like milliseconds. All information I have is the pulse test and short circuit test of the resistor.
Thanx

 

[MrAl]

Hi again,


Ok, so which resistor are you most interested in finding this information about, is it the 50 watt 25 ohm resistor, or the 1.8k resistor?

Also, what kind of resistor is this resistor, ie ceramic, TO220 type, etc. Is a part number for this resistor available?

 

[roozbehsf]

Hello
I want to find out these information about the 25ohm 50W resistor. It is a wire-wound resistor and the only information available for that is the result of the pulse test and the short circuit test as below.
1. Pulse test: the resistor can withstand max 20 pulses with the amplitude of 400v. ON duration: 25ms, OFF duration: 2500ms
2. Short circuit test: the resistor can withstand max 5 pulses with the amplitude of 400v. ON duration: 300ms, OFF duration: 700ms
Do you think these results are enough to estimate something or not?!
If yes, then how exactly?

Thank you

 

[MrAl]

Hi again,


When you say "Pulse Test" do you mean that the resistor is being supplied with 400v pulses for the ON duration and zero voltage for the OFF duration?

If so, then what do you mean by the "Short Circuit Test" where it appears to be getting pulses as well?

I think these tests would be showing us the heat capacity of the device and how it cools down, so we might be able to do this knowing that information. But i'd like to see you clear up what the Short Circuit Test is really doing, what the connections to the resistor are. From what i understand so far, these are tests with the resistor only and a voltage supply (and no capacitor or anything else in the circuits).

The goal then will be to apply the results of these tests to the new circuit that actually does have a capacitor in it.

 

[roozbehsf]

Yes, you are correct about the pulse test. These are the test that made by the supplier of the resistor and I have no detail information about them.
Unfortunately there are no informtio available about the amount of load in the pulse test. And I guess the short circuit test, as it's name tells us, should be applied without any load. Since the supplier made these tests so there shouldn't be any capacitances in those tests.
What I want to calculate and confuses me is to know under which condition the resistor would burn up!

Can you tell me more that how these tests show us the heat capacity of the resistor? because I think if we have the thermal capacity then we can calculate a safe condition for the resistor according to the power consumption of the resistor.

Thank you

 

[MrAl]

Hi again,


Well maybe this is even simpler than that. The reason i say this now is because when i calculate the time constant of the circuit and multiply that by 5, i see that the cap charges up in 125ms which is twice as fast as the longest time period in one of the pulse tests. This means the resistor will charge the cap, and after that it doesnt matter anymore what the switch does. This is because the cap charges up and it takes a full 1.8 seconds to discharge the cap by about 250 volts or so, so the next pulse becomes only 250v instead of 400v. So it looks like this particular circuit can take any pulse width or duration that you can throw at it. We're lucky here in that the discharge resistor is as high as 1.8k.

If you have a particular pulse duty cycle you would like to test on this circuit we can do that next. Just for a simple example, 100ms on, 500ms off.


In the attachment there is shown a test set. Various duty cycles are tested and the average power calculated at the end of 2000 seconds for each entry. Keep in mind this chart shows results from some 500 thousand calculations. How this test set is generated is as follows...

1. Start with a zero cap voltage Vc=0 and Vcc=420 volts, and an 'on' time of 100us and total period of 200ms.
2. Generate the first charge cycle using the equation for a charging cap with TWO resistors, calculating the new cap voltage Vc.
3. Generate the first discharge cycle using the equation for a discharging cap with ONE resistor, calculating the new cap voltage Vc.
4. Do steps 2 and 3 ten thousand times, noting the last charge voltage Vc1 and last discharge voltage Vc2.
5. Calculate the duty cycle D, calculate the power P from Vcc and the last Vc1 and Vc2, calculate the average power Pavg, tabulate.
6. Step the 'on' time by 100us and repeat steps 1 through 5, tabulating each Pavg result.

Finally, compare all the Pavg results looking for the highest value. Note that this is the entry for 2.7ms which generates an average power of 24.186 watts. This tells us that with the duty cycle that produces the highest power we will see less than 25 watts in the resistor. Since it is a 50 watt resistor the power rating for this resistor was a very good choice.

The other way to do it is to generate a series from the two equations for charge and discharge, then try to find a closed form for the series, then calculate the average voltage across the cap, then using the duty cycle calculate the average power in the resistor.


Table:

Ton       Time      Vc1    Vc2     Pavg     D
--------  ------    -----  -----   ------  -------
0.000100  2000.0     15.4   13.8    3.287  0.000500
0.000200  2000.0     29.8   26.7    6.138  0.001000
0.000300  2000.0     43.3   38.8    8.617  0.001500
0.000400  2000.0     55.9   50.1   10.775  0.002000
0.000500  2000.0     67.8   60.7   12.656  0.002500
0.000600  2000.0     79.0   70.7   14.296  0.003000
0.000700  2000.0     89.5   80.1   15.728  0.003500
0.000800  2000.0     99.5   89.0   16.977  0.004000
0.000900  2000.0    108.9   97.5   18.067  0.004500
0.001000  2000.0    117.8  105.5   19.018  0.005000
0.001100  2000.0    126.3  113.1   19.845  0.005500
0.001200  2000.0    134.3  120.3   20.564  0.006000
0.001300  2000.0    141.9  127.1   21.188  0.006500
0.001400  2000.0    149.2  133.6   21.727  0.007000
0.001500  2000.0    156.2  139.9   22.192  0.007500
0.001600  2000.0    162.8  145.8   22.590  0.008000
0.001700  2000.0    169.1  151.5   22.929  0.008500
0.001800  2000.0    175.2  156.9   23.215  0.009000
0.001900  2000.0    181.0  162.1   23.454  0.009500
0.002000  2000.0    186.5  167.1   23.652  0.010000
0.002100  2000.0    191.9  171.9   23.813  0.010500
0.002200  2000.0    197.0  176.5   23.940  0.011000
0.002300  2000.0    201.9  180.9   24.037  0.011500
0.002400  2000.0    206.6  185.2   24.108  0.012000
0.002500  2000.0    211.2  189.2   24.154  0.012500
0.002600  2000.0    215.6  193.2   24.180  0.013000
0.002700  2000.0    219.8  197.0   24.186  0.013500
0.002800  2000.0    223.8  200.6   24.175  0.014000
0.002900  2000.0    227.8  204.1   24.148  0.014500
0.003000  2000.0    231.6  207.5   24.108  0.015000
0.003100  2000.0    235.2  210.8   24.056  0.015500
0.003200  2000.0    238.7  214.0   23.992  0.016000
0.003300  2000.0    242.2  217.1   23.919  0.016500
0.003400  2000.0    245.5  220.1   23.837  0.017000
0.003500  2000.0    248.7  223.0   23.747  0.017500
0.003600  2000.0    251.8  225.8   23.650  0.018000
0.003700  2000.0    254.8  228.5   23.546  0.018500
0.003800  2000.0    257.7  231.1   23.438  0.019000
0.003900  2000.0    260.5  233.6   23.324  0.019500
0.004000  2000.0    263.3  236.1   23.206  0.020000
0.004100  2000.0    265.9  238.5   23.084  0.020500
0.004200  2000.0    268.5  240.8   22.959  0.021000
0.004300  2000.0    271.0  243.1   22.832  0.021500
0.004400  2000.0    273.5  245.3   22.701  0.022000
0.004500  2000.0    275.8  247.5   22.569  0.022500
0.004600  2000.0    278.1  249.5   22.434  0.023000
0.004700  2000.0    280.4  251.6   22.299  0.023500
0.004800  2000.0    282.6  253.5   22.161  0.024000
0.004900  2000.0    284.7  255.5   22.023  0.024500
0.005000  2000.0    286.8  257.3   21.884  0.025000