Ohms & Impedance

[ToddB66]

Dear friends,

Is it possible to convert Ohms to Impedance and vice-versa mathematically ? If so, I need the formulas please.

Thanks much !

Todd

[bbsailor]

Dear friends,

Is it possible to convert Ohms to Impedance and vice-versa mathematically ? If so, I need the formulas please.

Thanks much !

Todd

Todd,

The simple answer is no.

Ohms are measured at DC or direct current and it only varies slightly with temerature.

Impedance ohms called "Z" varies with frequency and the magnetic properties of the coil's core: air, ferrite or laminated metal.

bbsailor

[Carl-NC]

Todd,

Resistance (R, ohms) is the Real part of Impedance (Z, ohms). There is an Imaginary part called reactance (X), which is dependent on frequency. Mathematically,

Z = R + jX

If there is no reactive part, then Z = R.

- Carl

[ToddB66]

Todd,

The simple answer is no.

Ohms are measured at DC or direct current and it only varies slightly with temerature.

Impedance ohms called "Z" varies with frequency and the magnetic properties of the coil's core: air, ferrite or laminated metal.

bbsailor

bbsailor.........Thanks for the info.!

Todd

[ToddB66]

Todd,

Resistance (R, ohms) is the Real part of Impedance (Z, ohms). There is an Imaginary part called reactance (X), which is dependent on frequency. Mathematically,

Z = R + jX

If there is no reactive part, then Z = R.

- Carl

Carl.........Thanks for the formula ! Does the j stand for frequency, in other words, frequency times reactance ?

Regards,

Todd

[J_Player]

Hi Todd,
Calculating impedance can be a complicated task when there are a number of capacitances and inductances involved. The math requires some advanced methods beyond simple algebra. The j you are asking about is defined mathematically as a number that when multiplied times itself will equal -1. This falls in the category of imaginary numbers that are used for figuring impedance, while pure resistance is figured with real numbers that can be dealt with using ordinary algebra. When we combine imaginary numbers with real numbers to find impedance, we end up using what are called complex numbers that take most people some time to learn. This is why bbsailor said the simple answer is no for converting ohms to impedance.

The not so simple answer is the ohm value can be calculated for a given frequency, but it can become involved. Here is a page that shows how the formulas work to figure impedance: http://hyperphysics.phy-astr.gsu.edu...ric/imped.html

Best wishes,
J_P

[Qiaozhi]

Carl.........Thanks for the formula ! Does the j stand for frequency, in other words, frequency times reactance ?

Regards,

Todd

Hi Todd,

I bet you wish you'd never asked this question.

Let's try and explain in simple terms:

If you've ever tried to solve a quadratic equation, you will quite likely have found that the square root term sometimes contains a negative number. Now how can you find the square root of a negative number? Lets say the square root term is sqrt(-64). Is the answer +8, -8, or neither?

The answer is neither, because the square of both +8 and -8 is +64, not -64. However, if we note that -1 * 64 = -64, then we can take the square root of 64. However, we're still left with sqrt(-1). That's what the j term stands for. i.e. j = sqrt(-1). So the answer to sqrt(-64) is j8. That is, sqrt(-1) * 8.

Hmmm... so what's the point of this?

Quite often the answer will be something more like 3 + j2, where there is a real part (3) and an imaginary part (j2). To understand what this looks like, you can plot this on a graph. This is known as an Argand diagram. You would plot the real part on the x-axis and the imaginary part on the y-axis. Rather than referring to the resultant point on the graph by its cartesian coordinates (i.e. x and y) you can also draw a line from the origin (0,0) to the point and measure the length. The line also makes an angle with the x-axis. This line is known as a vector, that has both magnitude (length of line), and phase (angle made with the x-axis).

So, is this just some mathematical nonsense, or is there a real purpose to this?

In electronics, the use of these complex numbers (such as 3 + j2) is commonplace, especially where impedance (Z) is involved. If there is no imaginary part, then the real part represents a resistance. If there is an imaginary part, then the number represents a vector with both magnitude and phase. With regard to impedance, the x-axis represents the resistive part, and the y-axis represents the reactive part.

Clear as mud?

[ToddB66]

Hi Todd,

I bet you wish you'd never asked this question.

Clear as mud?

Qiaozhi........Yes & Yes !

Thank God for people like yourself, otherwise we never would have stepped on the moon !

I really appreciate the time you spent creating that reply and respect your knowledge.

Like you suspected, most of it went right over my head !

As the song goes "You got to know when to hold'em, know when to fold'em".
I think it's time for me to get out of this card game.

Maybe someone else will be able to understand and use the information though.

Best Regards,

Todd

[ToddB66]

Hi J_P !

Thanks for the explanations. I appreciate the time you spent.

The link you provided left me flabbergasted !

So I'll go with bbsailor's simple answer.

Todd

[mikebg]

Hi hams! Why you dont read WEB? For example
http://en.wikipedia.org/wiki/Electrical_impedance
Carl, the Real part of impedance is also dependent on frequency.
Mike ***

[Carl-NC]

Carl, the Real part of impedance is also dependent on frequency.

You'll have to explain that one to me.

[mikebg]

Explanation:

Why the real part of impedance depend on frequency?

The knowledge of impedance theory helps to metal detector designers to project target identifying and discriminating apparatus. Every metal detecting system includes a two-port subsystem " sensor & target". TX current (or magnetic field) exists in input port of the subsystem and an EMF (voltage) induced in RX coil exists in output port. That's why the frequency response of this subsistem is dimensional - transfer impedance Z.
Despite my poor english, soon I'll try to explain (with drawing) transfer impedance of target permeability and conductivity in the forum thread "Frequency response of target". For the present I'm trying to explain here without drawings why and when the real part of impedance Z depends on frequency:
The Real part of impedance or admittance is an even transfer function expressing energy loss. The right term for "energy loss" is "exergy loss" or “dissipation” because exergy (for example electricity) transforms in anergy (heat).
The Imaginery part of impedance is an odd function expressing lossless energy transform – one kind of exergy (for example magnetic field), transforms in another kind of exergy (electric field) and vice versa.
The real part of impedance is dependent on frequency when the exergy dissipates by whatever frequency depended process (skin effect, hysteresis loss, dielectric heating).
-1st example: the target near a metal detecting sensor is lossless ferrite core. The transfer impedance is pure imaginary. The phase of lossless ferrite signal is independent from frequency. EMF induced in RX coil by ferrite core is always in quadrature (90 degree) to TX coil current. Because of quadrature, it is impossible to distinguish in frequency domain the lossless ferrite signal from EMF induced by positive mutual iductance between TX and RX coil. The frequency response of mutual inductance is also in quadratire. The difference between both signalls occurs in the time domain. The parasitic modulation of TX field caused by TX coil movement (change of height and cange of ground properties), limits detectors ability to recognise faint meteorite signals in frequency domain.
-2nd example: the target is lossy ferrite, its conductance is also zero. Transfer impedance isn't pure imaginery; it has Real part increasing phase lag. The phase lag is more than quadrature to excitating magnetic field (TX current). The phase lag of lossy ferrite is also independent on frequency; that means both real and imaginary part of the transfer impedance increase with frequency in equal scale. Since mutual impedance has no real part depending on frequency, it is possible even in frequency domain to distinguish signal of "lossy hot rocks" from parasitic TX modulation.
-3rd example: the target is nonferrous but has conductivity. The Real part of transfer impedance increases nonlinear with frequency. Real part has maximum at "cutoff" 3dB frequency.
It is dificult to explain this without drawing (spectral response in complex impedance plane). Unfortunately, I can't find in the WEB suitable resources to reference. That's why I started the tread "frequency response" in february. The WEB resources of NDT "eddy current testing" and of Wikipedia are also deficient in drawings.Then what follows?… DIY drawings!
For the present I'm stopping to write because I'm starting to draw.
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