DC Transient RL Circuit - Current Decay

[LADransfield]

If I have a circuit with

R = 1Ω
L = 300μH
V = 20V
i₀ = 5A

I know that I can use the equation at the bottom of page 13 to calculate the current rise given any starting current and input voltage:

i(t) = (V/R)[1-e^-t/τ] + i₀e^-t/τ

This is fine, and stops increasing at 20A as expected, but then how would I (if I need to) arrange the equation so that it works in a similar way for decay? Say I was starting at a current of 15A, with a driving voltage of 10V?

I know that if I use:

i(t) = (V/R)[e^-t/τ]

I will start decaying at 10A down to 0A, but I'm interested in being able to specify a negative voltage to drive the decay faster, with a variable starting current.

Thanks in advance for any advice!

*edit*
Also, how would I work out when it is best to switch between building and decaying current? Would it just be when |V/R| > |i(t)| is less than 0, I build, and when |V/R| < |i(t)| I decay?

Thanks again

 

[axemaster]

I don't understand the problem. That equation appears to work regardless of "rise" or "decay", and regardless of what types of inputs you use (provided they are not dynamic).

 

[LADransfield]

I have been using transient inputs, though every time my input changes, I have resent my t back to 0 and begun recounting, so the dynamic input shouldn't be a problem

Compared to simulation from ANSYS Maxwell and from test data, this appears to be calculating results which decay much slower, though rise appears relatively similar

 

[axemaster]

The equation definitely doesn't have any differences between rise/fall times, it is inherently symmetric. The only thing I can think of is that perhaps you are calculating τ incorrectly? It should be τ = L/R.

This equation will work fine for multiple step transients provided it has time to fully settle before applying the next one. If you are trying to calculate transients that are something other than step changes, you will want to solve the general differential equation.

 

[alphy]

for any help!

I would first start by acknowledging the information provided and understanding the circuit setup. The DC transient RL circuit consists of a resistor (R), inductor (L), and a voltage source (V) with an initial current (i0). The equation provided on page 13 allows for the calculation of current rise given any starting current and input voltage. However, the individual is interested in understanding how to arrange the equation for current decay with a variable starting current and a negative voltage to drive the decay faster.

To calculate current decay, the equation can be modified to include a negative voltage (V) and a variable starting current (i0) as follows:

i(t) = (V/R)[1-e-t/τ] + i0e-t/τ

This equation will allow for the calculation of current decay starting at a specified current (i0) and driven by a negative voltage (V). The negative voltage will accelerate the decay of the current, resulting in a faster decrease.

To determine when to switch between building and decaying current, it would be best to consider the magnitude of the voltage (V) and the magnitude of the current (i(t)). When |V/R| is greater than |i(t)|, the circuit is in the building phase. When |V/R| is less than |i(t)|, the circuit is in the decaying phase. Switching between the two phases can be done at any time, but it would be most effective to switch when the current is at its maximum or minimum value.

In summary, the equation provided can be modified to calculate current decay with a variable starting current and a negative voltage to drive the decay faster. The switch between building and decaying current can be determined by comparing the magnitude of the voltage and current.