Inductance Current
Inductance Current
(OP)
The relation between voltage and current for an inductor is given by:
v = L . di/dt
I think this relation is valid only in steady state periodic cyclic operation and provided that the circuit contains a resistive element.
My question now :Why a resistive element should be contained in the circuit to make this relation valid ?
v = L . di/dt
I think this relation is valid only in steady state periodic cyclic operation and provided that the circuit contains a resistive element.
My question now :Why a resistive element should be contained in the circuit to make this relation valid ?





RE: Inductance Current
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
There has been some success with super conductive magnet coils but although these coils are inductive and without resistance the nature of them is such that there is no variation in the current under normal operating conditions. Actually the only way to change the current is to introduce some resistance into the circuit by heating a small portion of the superconductive coil to drive it out of the superconducting region.
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Inductance Current
RE: Inductance Current
It is about reality. Not that the relation doesn't hold.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
But perhaps the simulator is working. Zero resistance would be expected to return a value of zero in many of your equations. You may get a few divide by zero errors also.
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Inductance Current
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
v = - L.di/dt ???
What is the secret in that resistor ???
RE: Inductance Current
For the steady state solution, Ohm's law is valid and if you make R in the I=E/R equal to zero, you will get divide by zero.
Nothing to it. Just plain elementary physics and math.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
RE: Inductance Current
You may need to study how simulators work.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
Suppose a voltage of train of square wave of pluses (with only positive polarity)applied to a pure inductance,and according to the equation:
V = N.do/dt , whare o is the flux
The flux wave form will start from zero and increases linearly to its positive peak and the decreases to zero again and and then back to its positive peak ,amd never goes to negative polarity.
But because of a resistor in the circuit the flux will swing between positive and negative peaks.
My question again ,why a resistor in the circuit makes that difference ?
RE: Inductance Current
1 - a steady state solution
2 - a transient solution
I assume your square wave averages to zero (otherwise if you apply it to inductor alone, the solution would grow to infinity). This problem then acts very similar to sinusoidal excitation
The transient solution has a dc component.
When a resistor is present, the steady state solution does not have a dc component. When the transient component decays to zero with time constant L/R, all that is left is the steady state solution with no dc current.
The simulator is telling you the correct solution. Try to solve the problem yourself and compare. If the square wave problem is too hard, try it with sinusoidal source.
=====================================
(2B)+(2B)' ?
RE: Inductance Current
By ideal inductor, I mean resistance neglected, saturation neglected, hystesis neglected etc. When you make those assumptions what is left is the ideal inductor which follows v = L*di/dt under all circumstances by definition
=====================================
(2B)+(2B)' ?
RE: Inductance Current
RE: Inductance Current
RE: Inductance Current
The initial pulse will be enough to create some current in your R-L circuit. Can that current continu flowing forever?
I hope you answer is No. The resistor is dissipating energy and there is no input from the source, so the system loses energy and must eventually end in zero state. Once the voltage is switched off, the current decays according to I(t) = I(t0)*exp(t-t0)
You can think of your square wave as superposition of a series of pulses. The dc component is a characteristic of the initial startup transient and it decays to zero just like our single pulse. What is left after a long period of time is the steady state component which has no dc in an R-L circuit.
=====================================
(2B)+(2B)' ?
RE: Inductance Current
Once the voltage is switched off, the current decays according to I(t) = I(t0)*exp(t-t0)
should've been:
Once the voltage is switched off, the current decays according to I(t) = I(t0)*exp((t-t0)*R/L)
=====================================
(2B)+(2B)' ?
RE: Inductance Current
RE: Inductance Current
Your 23 Jan 11 11:36 does not say anything new. It is the same question as before - simply because there is a linear and direct dependence between current and flux in an ideal coil.
So even if you try to make us understand, which you really do not need to, it would be much better if you tried to understand that what you have observed and what Pete, Bill and I are telling you is the truth.
Endless discussions like this one will only diffuse your field of view and are also rather tedious.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
RE: Inductance Current
What can you do, Pete?
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
RE: Inductance Current
If you want to study the inductor theory without resistance look at this site:-
h
desertfox
RE: Inductance Current
=====================================
(2B)+(2B)' ?
RE: Inductance Current
=====================================
(2B)+(2B)' ?
RE: Inductance Current
Tip. Long before you get near zero inductor resistance the source effective resistance will become significant in the real world.
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Inductance Current
R=0 has a dc component that does not decay
R=0.2 has a very noticeable decaying dc component
R=10 has no noticeable dc component (it decays before the 1st peak)
Compare it against your own computer simulator and mental simulator.
Note there is a "phase angle" inherent in the definition of Vs(t) that affects the dc offset results. I think if Vs had started with a half-width pulse instead of a full-width pulse, there would have been no dc offset.
=====================================
(2B)+(2B)' ?
RE: Inductance Current
May i ask you where i can get a copy of the simulator software you have ?
RE: Inductance Current
I think Mathcad and Mathematica are similar although I've never used them.
If simulation is what you're after, there are a lot of possibilities like Pspice, Matlab ODE routines like ODE45, free Matlab clones (Octave, Sci-lab) etc. I'm partial to using a general ODE solver rather than circuit solver myself. Maybe others will chime in on the simulator software question or direct you to a previous thread on that.
=====================================
(2B)+(2B)' ?
RE: Inductance Current
I assume that the student version of Maple (and probably also the 'pro' version) has a minimum default value for the first order term. Without it, you get lots of questions like the one that caused this thread. In pure circuit simulators, there's a nanoohm-microohm built into the reactive components so you do not get the divide-by-zero message.
Or does Maple have any other mechanism that catches that?
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
Maple have a number of options for dsolve... if you want a specific numeric solution method there are extra arguments to dsolve, but if you don't use any it uses a symbolic method and the solution is symbolic:
i.e. dsolve({subs({L=1,R=10},DiffEqn),i(0)=0},i(t)) outputs the following exact algebraic solution, just as if you had solved it by hand:
CODE
+ 1/5 Heaviside(t - 2) - 1/5 Heaviside(t - 3)
+ 1/5 Heaviside(t - 4) - 1/5 exp(-10 t + 140) Heaviside(t - 14)
- 1/5 Heaviside(t - 5) + 1/5 Heaviside(t - 6)
- 1/5 Heaviside(t - 7) + 1/5 Heaviside(t - 8)
- 1/5 exp(-10 t + 100) Heaviside(t - 10) - 1/5 Heaviside(t - 9)
+ 1/5 Heaviside(t - 10) - 1/5 Heaviside(t - 11)
+ 1/5 exp(-10 t + 10) Heaviside(t - 1)
- 1/5 exp(-10 t + 200) Heaviside(t - 20)
+ 1/5 exp(-10 t + 190) Heaviside(t - 19)
+ 1/5 exp(-10 t + 70) Heaviside(t - 7)
+ 1/5 exp(-10 t + 130) Heaviside(t - 13)
+ 1/5 exp(-10 t + 50) Heaviside(t - 5)
+ 1/5 exp(-10 t + 30) Heaviside(t - 3)
- 1/5 exp(-10 t + 40) Heaviside(t - 4)
+ 1/5 exp(-10 t + 110) Heaviside(t - 11)
- 1/5 exp(-10 t + 60) Heaviside(t - 6) + 1/5 Heaviside(t - 12)
- 1/5 Heaviside(t - 13) + 1/5 Heaviside(t - 14)
- 1/5 Heaviside(t - 15) - 1/5 exp(-10 t + 120) Heaviside(t - 12)
+ 1/5 Heaviside(t - 16) - 1/5 Heaviside(t - 17)
- 1/5 exp(-10 t + 160) Heaviside(t - 16) + 1/5 Heaviside(t - 18)
- 1/5 Heaviside(t - 19) + 1/5 Heaviside(t - 20)
+ 1/5 exp(-10 t + 150) Heaviside(t - 15)
+ 1/5 exp(-10 t + 170) Heaviside(t - 17)
+ 1/5 exp(-10 t + 90) Heaviside(t - 9)
- 1/5 exp(-10 t + 20) Heaviside(t - 2)
- 1/10 exp(-10 t) Heaviside(t)
- 1/5 exp(-10 t + 80) Heaviside(t - 8)
- 1/5 exp(-10 t + 180) Heaviside(t - 18)
The forward Euler method is an example of explicit:
X(t+h) = X(t) + f(X(t))
It will not fail as long as there is a solution f(X(t)) which does not blow up. An iterative explicit variable step size routine would decrease step size to the minimum around the step-changes in V(t), but wouldn't have any problems generating a solution.
Matlab's ode45 is a more common example of explicit method.
The backward Euler method is an example of implicit method:
X(t+h) = X(t) + f(X(t+h))
it is not a straightforward calc since X(t+h) is only implitly defined.
I think most circuit solvers use the trapezoidal method which is also an implicit method:
X(t+h) = X(t) + 0.5*(f(X(t) + f(X(t+h))
It is also an implicit technique since there is no explicit formula for X(t+h).
For an inductor
I(t+h) = I(t) + 0.5*(V(t) + V(t+h))/L
The problem is V(t+h) is not necessarily known without I(t)
If we solve for 2 variables I(t+h) and V(t+h) in terms of the variables I(t), V(t), we have a relationship between I(t+h) and V(t+h) in terms of known quantities (V(t), I(t), L). This resembles an impedance relationship in terms of h and can be collected together in an impedance matrix and inverted. I assume the inversion step is where the problem occurs in circuit solvers which use an implicit integration method. Again should be no problem for explicit methods.
Sorry if this is more than you wanted. If you have any insight on the error you were talking about I'd be interested to hear... I was guessing as to the cause (matrix inversion)
=====================================
(2B)+(2B)' ?
RE: Inductance Current
Looks like Maple handles it well.
Thanks.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
"Another benefit of these new simulation devices is that convergence problems are easier to avoid since they, like the board level component the model, have finite impedance at all frequencies."
I think that says it quite well. Making all components having finite impedance at all frequencies - also DC. That means that there are no zero ohm inductors, among other things.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
What that material is?
What about the cost ?
RE: Inductance Current
Same problems today. Only that temperature can now be a lot higher. But still quite cold. Sensitivity to magnetic flux still there. Not good in a coil supposed to produce a magnetic field.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
2009 news: "[successful] full-power testing of the world's first 36.5 megawatt (49,000 horsepower) high temperature superconductor (HTS) ship propulsion motor..."
See also: amsc.com
RE: Inductance Current
These units would withstand the intense magnetic field but an upset in the field would often drive part of the coil into the ohmic conduction range. This would instantly avalanche and the whole coil would go into ohmic conduction. The liquid helium would boil and often a part of the safety valve would become impaled in the ceiling. The scientific name for this event is a "Quench". NMRs for student use may have several holes in the ceiling from quenches.
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Inductance Current
There's an installation at Holbrook substation on Long Island, New York, running "138kV at 2400A ~574MVA".
RE: Inductance Current
Now what if we think about the computation error in one time-step as a dc offset for the next step... In the case of the R-L system, the effect of an error at time t will be no longer evident after awhile... for example after 10 time constants.. But the effect of errors in the L-only circuit remain forever for the entire simulation. So if I run the simulation for a very long time, the R-L circuit has only errors accumulated from the last 10 time constants for example, whereas the L circuit has errors accumulated from each step of the entire simulation.
The errors at each step come from local truncation error (approximating Taylor series with some kind of truncation used by the algorithm) as well as rounding errors. If the errors all tend to add in the same direction, then clearly the L-only case will accumualte more errors. But even if the errors vary randomly poisitive and negative, the standard deviation of the error will be much larger for the L-only case than for the R-L case (if we run the experiment many times, the error averages to zero but the spread of errors is much larger for the L-only case).
I did a small experiment to check if this would cause a problem (attached). It shows an L-only circuit driven by a 50hz sinusoid for 25 seconds (1250 cycles) using a 0.002 sec timestep. The closing angle and magnitude are set up such that the magnitude of the ideal current waveform varies between 0 and 2 (dc offset of 1). A Runge-Kutta 4th order method is used for simulation (see Runge-Kutta tab for equations from wiki... pretty simple). You can view in tab "main" the plot of the results between 24.5-25 seconds and the current magnitude is exactly between 0 and 2 as expected from ideal solution. In fact if you look at the time 25.000, we expect the value is exactly zero and we read the numerical value from the spreadsheet to be 7E-13. I think for most purposes it is not an error to concern ourselves with, even though we accumulated errors over a very long simulation.
Other than the above concern which is shown to be relatively minor, I can't see any other problems with this L-only configuration.
My best guess is that whatever reason Spice forbids this L-only configuration has more to do with the particular algorithm used by Spice than with problems inherent in the circuit configuration itself. But I don't know anything about Spice.
=====================================
(2B)+(2B)' ?
RE: Inductance Current
I don't know if you guys were surprised, but I was very surprised to get such a low number for "accuracy" in the my R-L simulation posted just above, especially considering I was using such a big step size (my first reaction was: D*mn!.... that Runge-Kutta is amazing). Now I have studied it a little more and it turns out there is more to the story....
In general (from textbooks), there are 2 types of errors that can occur at a given step:
1 – Roundoff error – independent of step-size. It is assumed to vary randomly from step to step (not correlated with previous steps). Since it varies randomly, by the Central Limit theorem, we can predict that the standard deviation of the cumulative roundoff error after N steps is sqrt(N)*sigma where sigma is standard deviation of roundoff error for one step and N is number of steps (N assumed large for C.L.T.)
2 – "Local Truncation Error". This is not "truncation" as in roundoff, but "truncation" as in truncating the infinite Taylor series associated with the exact differential equation/solution down to a finite Taylor series associated with our approximate algorithm/solution. The magnitude of this particular error increases with step size. In contrast to roundoff error, the variation in LTE between steps might not be random (in this case there is a definite non-random pattern as we will discuss.
Now let's analyze how these two errors might appear in our R-L simulation example:
1 - First roundoff error. Excel uses double precision, where the relative error (of one step) will be on the order of 1E-15 to 1E-14. Since the variable varies between 0 and 2, averaging about 1 that is also our absolute error. For the previous example 25 seconds sampled every 0.002 seconds, it was 12,500 steps and (by Central Limit Theorem) we expect the standard deviation of the accumulated roundoff errors at the end to be 1E-15 to 1E-14 * (sqrt(12,500)) = 1E-13 to 1E-12. So the observed value of 7E-13 that we saw at t=25.000 seconds was very reasonable considering accumulated roundoff error alone.
2 - Next let's discuss Local Truncation Error. It could probably be analyzed mathematically, but I took a different approach... attached I have modified my spreadsheet to add a plot labeled "Error" based on numerical comparison of the simulation output to the true known solution I(t) =1-cos(2*pi*50*t). On the "Error" plot graph you see a sinusoid which varies from 0 to –0.0001. The error plot is periodic at 50hz and it roughly reaches 0 whenever time t is an exact multiple of 1/50hz = 0.020 sec. Also I made the step size an irrational number sqrt(3)/1000 to make sure relationship between step size and exciting frequency is not causing any irregularity (it is not). However if you vary the step size (cell D7, labeled "dt"), you will see that the magnitude of the error plot goes up when you increase dt and goes down when you decrease dt.... which is an expected characteristic of Local Truncation Error.
The above facts lead us to the following conclusions about this particular R-L simulation:
A – The global truncation error (sum of accumulated local truncation errors) is many many order of magnitudes higher than the roundoff error for this simulation.
B – The global truncation error in this particular simulation is periodic at frequency 50hz, which implies the local truncation error is periodic at 60hz. In retrospect, it is not surprising that the error associated with truncating a sin wave at a finite number of terms is itself periodic.
C – The periodicity of the truncation errors prevents them from accumulating to very high values during a very long simulations (global truncation error varies between 0 and some max number, but doesn't tend to increase without bound over time). However we should not expect that to be the case for general excitations other than sinusoidal. I am envisioning I could create a problem using a sawtooth voltage wave where the rising edge is given by (t-tstart)^5 and the falling edge drops sharply, and we add a constant to make the average value of the voltage waveform zero... I think the local truncation errors will be all the same sign and the global truncation error will continually grow with time during a long simulation. (If you see another post appear in this thread, it is probably me trying that idea out).
D – The previous post examined the error at a time t=25.000 sec, exactly divisible by 0.020 when the global truncation error happened to be zero, so results (1E-12 corresponding to accumulated roundoff) were a "little" misleading
=====================================
(2B)+(2B)' ?
RE: Inductance Current
=====================================
(2B)+(2B)' ?
RE: Inductance Current
RE: Inductance Current
TTFN
FAQ731-376: Eng-Tips.com Forum Policies
Chinese prisoner wins Nobel Peace Prize
RE: Inductance Current
=(V_*SIN(W_*($B18+dt_))-R_*($C18+[b]dt_/2[]*F18))/L_
should have been:
=(V_*SIN(W_*($B18+dt_))-R_*($C18+dt_*F18))/L_
But it doesn't make any difference in the solution when R=0, which was the case for everything I discussed above.
Yes, the spreadsheet used a fixed-step size Runge-Kutta 4th order method shown here:
http:/
For circuits with more than one element, you have to put them into the form: d/dt(x(t)= f(x(t),t) where x is a vector of state variables. Generally that is easily done by making your inductor currents and capacitor voltages the state variables. The extension from scalar to vector case should be fairly intuitive. It does get a little cumbersome to do it in a spreadsheet which doesn't handle vector variables, so I use vba when I have more than one state variable. Beyond the fixed-step size Runge-Kutta 4th order method, it is very common to use the Runge-Kutta Felhburg (spelling?) method which adjusts the step size to control the estimated local truncation error. It determines the local truncation error of the 4th order RK by comparing it to a 5th order RK method. That's what Matlab ODE45 uses. I have a spreadsheet that does something like that using vba which I can post if you want, but if you don't know how to program vba (to define the slope function) it won't do you any good.
Any numerical analysis textbook will cover the above and a lot more about numerical solution of Ordinary Differential Equation initial value problems such as this.
I can't help you with Spice.
=====================================
(2B)+(2B)' ?
RE: Inductance Current
Driving waveform is a sinewave and phase shift is zero. That results in an initial DC component that seems never to die because of the hefty L/R time constant (1 megaseconds). If you let the simulation run long enough, you will see the DC component decaying.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
(tolerance times maximum voltage divided by maximum current)10 (or 100)
shall read
(tolerance times maximum voltage divided by maximum current)/10 (or 100)
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
The initial pulse will be enough to create some current in your R-L circuit. Can that current continu flowing forever"
I come late to the party, but excuse me, if you are talking a pure ideal inductor, the answer is yes, the current will go on for "the rest of eternity"
RE: Inductance Current
=====================================
(2B)+(2B)' ?
RE: Inductance Current
"electricpete,what is the transient response of a pure inductance to a square wave ? With no resistor included".
YOUR ANSWER
"Let's look at a simpler excitation. Just apply a single pulse with your voltage source and then turn your voltage source back to zero for the rest of eternity.
The initial pulse will be enough to create some current in your R-L circuit. Can that current continu flowing forever?
I hope you answer is No.........................."
I didn't look further and never noticed the R_L you tossed in.
No wonder why the OP was confused, especially with all the extraneous irrelevant answers he was getting.
RE: Inductance Current
I do not think you are fair in that last comment.
The OP got lots of valid answers to his initial question. But he never bothered to try and understand what they said.
Did you read all those "extraneous irrelevant answers he was getting"? Your reading strategy ("I only looked at your first line" could perhaps benefit from a slight adjustment.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Inductance Current
To answer that question, you need to discuss both cases as I have done in this thread.
The question"electricpete,what is the transient response of a pure inductance to a square wave ? With no resistor included" was timestamped "23 Jan 11 12:09".
The post of mine addressing R-L circuit was timestamed 23 Jan 11 12:14. I was probably typing while he was posting because this was followup to an earlier point and not direct response to that question which I never saw.
The OP understood exactly what the R in R-L meant as he followed up with "I am agree with you electricpete in the case of a resistor exists in circuit ,but what would be the behavior if no resistor is there, just only pure inductance. " 23 Jan 11 12:49
Later, the OP has later acknowledged by help "Thanks pete,that is a perfect answer to my question."
Time to move on imo. Unless you would like to talk about R-L circuits or why Spice makes you put a resistor in there.
=====================================
(2B)+(2B)' ?
RE: Inductance Current
Good answers by you.
But in all fairness, the 1st poster nailed the rather trivial question and it should have ended right there. A lot of wasted ink.
RE: Inductance Current
In the shared interest of conserving electronic ink, may I suggest to move on? (unless there are other comments related to the questions raised in this thread).
=====================================
(2B)+(2B)' ?
RE: Inductance Current
=====================================
(2B)+(2B)' ?
RE: Inductance Current
=====================================
(2B)+(2B)' ?