Something Different:

[Hameedulla-Ekhlas]

ratuss:

Can we call a v(t) / i(t) a characteristic impedance or instantaneous impedance.

 

[drbond24]

Alright,

v(t) = 1.0v
i(t) = 0.0a

again for the same circuit, let

v(t) = 0.0v
i(t) = 1.0a

which result provides the impedance?

A voltage with no current is a generator with no load connected, so there is no impedance. I don't mean impedance is 0, I mean there is none. The answer is the null set.

A current with no voltage can't happen.

 

[rattus]

ratuss:

Can we call a v(t) / i(t) a characteristic impedance or instantaneous impedance.

Ham, not in general because only if the load is a pure resistance is this ratio constant. I would just call characteristic impedance Zo, and I would call z(t) nonsense.

The simple fact is that impedance and reactance are not defined for instantaneous equations. Furthermore, impedance and reactance are defined only for sinusoidal waveforms, and v(t) and i(t) may be of any shape such as step functions, sawtooth waves, etc.

The reason I started this post is that some believe this ratio is useful, and I wanted to disprove that belief.

Granted, a knowledgeable person can compute a value of Z from Vm and Im and can extract the impedance angle from the equations, but Z cannot be used with v(t) and i(t) unless Z=R.










Now

 

[rattus]

A voltage with no current is a generator with no load connected, so there is no impedance. I don't mean impedance is 0, I mean there is none. The answer is the null set.

A current with no voltage can't happen.

But it can and will if the current is leading or lagging! Remember these are not RMS values. They are functions of time which periodically have zero values.

 

[rattus]

v(t) = 1.0v
i(t) = 0.0a -------------------------this condition eq-1

again for the same circuit, let

v(t) = 0.0v
i(t) = 1.0a ---------------------------this condition eq-2

ratuss: Is that what you mean by eq-1

Ham, eqn. 1 is identified by "1)" next to the left margin.

 

[rattus]

Now in this circuit for t > 0, the value of v(t) / i(t) = ? for v(t) = 12 t > 0

Hom, this appears to be a differential equations problem where the excitation is a 12V step function. This is far removed from the subject of this thread. I will say though that v(t)/i(t) will not be a constant here and is therefore a useless concept.

 

[drbond24]

But it can and will if the current is leading or lagging! Remember these are not RMS values. They are functions of time which periodically have zero values.

If the current is leading or lagging then there is inductance and/or capacitance in the circuit. If there is inductance and/or capacitance in the circuit then there are complex numbers involved. If there are complex numbers involved, then the value i(t) cannot be real as you have asserted.

There is a paradox in your position which makes the question itself both useless and nonsense.

A kobayashi maru in Star Trek is cool and makes nerds like me excited. Here, its just silly.

 

[Smart $]

...

But for t > 0 v(t) / i(t) = z I have doubt in this. Because since we are in time domain and we have all R, L and C. R is ohm, L is mh, and C is micro F.
Now in frequency domain we change easily C and L to Xc or XL by only multiplying the jwL or jwC. How can you add in time domain C, L and R to say that v(t) / i(t) = z ? I may be confused or any idea. Hope to give some explaination.

But what I have seen the instantaneous impedance in signal analysis which is also called characteristic impedance. Even in signal or transmission line j cancells and we get simple real number with unit ohm

The thing about trying to evaluate impedance as a function of time using the step function is all you are doing is separating the transmission effects of impedance from the load effects of impedance. Consider that impedance (Z) includes R, C, and L. R by itself is still impedance when considering an AC circuit. The only differnece is that it does not cause a phase shift between voltage and current.

The other issue is that you are trying to relate v(t)/i(t) to Z. There is no direct relationship. The relationship is v(t)/i(t) = ?(t), where ?(t) is just an expression. There exists an indirect relation to Z as a function of time, and this is the only reason we have called it z(t). As I said previously, it is probably better referred to as Ω(t) or Req(t).

The best understanding comes from determining why v(t)/i(t) is not constant for situations other than θ = 0. Start by converting the complex-valued expression Ze^jθ to its real-valued sinusoidal function using Euler's formula, and then consider the real result when θ = 0 and θ = ?90?, the extremes, then values in between.

 

[Hameedulla-Ekhlas]

Ham, not in general because only if the load is a pure resistance is this ratio constant. I would just call characteristic impedance Zo, and I would call z(t) nonsense.

The simple fact is that impedance and reactance are not defined for instantaneous equations. Furthermore, impedance and reactance are defined only for sinusoidal waveforms, and v(t) and i(t) may be of any shape such as step functions, sawtooth waves, etc.

The reason I started this post is that some believe this ratio is useful, and I wanted to disprove that belief.

Granted, a knowledgeable person can compute a value of Z from Vm and Im and can extract the impedance angle from the equations, but Z cannot be used with v(t) and i(t) unless Z=R.

Now

I am completely agree with you in this concept and in transmission line and power flow SIL also we get just a constant real number and is called characteristic impedance when we make voltage constant at both ends.

 

[Hameedulla-Ekhlas]

But it can and will if the current is leading or lagging! Remember these are not RMS values. They are functions of time which periodically have zero values.

v(t) = 0.0v
i(t) = 1.0a ---------------------------this condition eq-2

voltage is equal to zero here it looks voltage source is zero and we have still current. But this can happen that we have capacitor in a circuit with initial charge.

 

[rattus]

If the current is leading or lagging then there is inductance and/or capacitance in the circuit. If there is inductance and/or capacitance in the circuit then there are complex numbers involved. If there are complex numbers involved, then the value i(t) cannot be real as you have asserted.

There is a paradox in your position which makes the question itself both useless and nonsense.

A kobayashi maru in Star Trek is cool and makes nerds like me excited. Here, its just silly.

Bondo, consider a 30 degree lag, then:

i(t) = Im[sin(wt -30)]

Now evaluate this at 30 deg,

i(30) = Im[sin(30 - 30)] = 0.0, that is all no phase angle.

The phase angle disappears when you evaluate i(t).

 

[Hameedulla-Ekhlas]

Hom, this appears to be a differential equations problem where the excitation is a 12V step function. This is far removed from the subject of this thread. I will say though that v(t)/i(t) will not be a constant here and is therefore a useless concept.

Ok but I gave an example in post 69 with a constant source and it was the concept of signal and characteristic impedance but I did not get any comment from you regarding that. So, I thought you might mean step function.

 

[rattus]

voltage is equal to zero here it looks voltage source is zero and we have still current. But this can happen that we have capacitor in a circuit with initial charge.

But what are the values of v(t) and i(t) for the two conditions? Are they constant? Are they zero? Are they something else.

 

[rattus]

Ok but I gave an example in post 69 with a constant source and it was the concept of signal and characteristic impedance but I did not get any comment from you regarding that. So, I thought you might mean step function.

Ham, actually you should have a switch in the circuit. This switch closes at t= 0+ to create the step function.

 

[Hameedulla-Ekhlas]

But what are the values of v(t) and i(t) for the two conditions? Are they constant? Are they zero? Are they something else.

Yes, I got it thanks they are contant

 

[Hameedulla-Ekhlas]

The thing about trying to evaluate impedance as a function of time using the step function is all you are doing is separating the transmission effects of impedance from the load effects of impedance. Consider that impedance (Z) includes R, C, and L. R by itself is still impedance when considering an AC circuit. The only differnece is that it does not cause a phase shift between voltage and current.

The other issue is that you are trying to relate v(t)/i(t) to Z. There is no direct relationship. The relationship is v(t)/i(t) = ?(t), where ?(t) is just an expression. There exists an indirect relation to Z as a function of time, and this is the only reason we have called it z(t). As I said previously, it is probably better referred to as Ω(t) or Req(t).

The best understanding comes from determining why v(t)/i(t) is not constant for situations other than θ = 0. Start by converting the complex-valued expression Ze^jθ to its real-valued sinusoidal function using Euler's formula, and then consider the real result when θ = 0 and θ = ?90?, the extremes, then values in between.

v(t) / i(t) = Z considered it as a intantaneous or characteristic impedance.

See rattus post number 123

 

[drbond24]

Bondo, consider a 30 degree lag, then:

i(t) = Im[sin(wt -30)]

Now evaluate this at 30 deg,

i(30) = Im[sin(30 - 30)] = 0.0, that is all no phase angle.

The phase angle disappears when you evaluate i(t).

What caused the 30 degree lag?

 

[rattus]

Yes, I got it thanks they are contant

No Ham, in one case the ratio is zero; in the other the ratio is infinity for the same circuit. The ratio is not constant.

 

[Hameedulla-Ekhlas]

Ham, actually you should have a switch in the circuit. This switch closes at t= 0+ to create the step function.

I reviewed your all posts and had missed one post in the middle I found something "NOTE TO ALL " post. Which changes all your first question to something else. So, according to that " NOTE TO ALL"
I am agree. I was always paying attention to the first post question.

 

[Hameedulla-Ekhlas]

No Ham, in one case the ratio is zero; in the other the ratio is infinity for the same circuit. The ratio is not constant.

But what are the values of v(t) and i(t) for the two conditions? Are they constant? Are they zero? Are they something else.

you asked the value of v(t) and i(t) which is already had given as a number and you did not mention the ratio. Ok but any way, thanks for all and you are right.