# Inductor Series Resistance?

Thread Starter

#### Schniz2

Joined Apr 15, 2010
22
I'm trying to calculate the ESR of my inductor, i calculated the inductance by connecting it in series with a 10k resistor and increasing the frequency of the function generator until the voltage across the resistor was half the input voltage, then used the formula L = R/(2*pi*f).

I was wondering if anyone knew a method of calculating the ESR of the inductor? I have an LCR meter but the current output is apparently too low to set up the flux.

Im operating a 10mH 5A common mode choke at 20kHz.

Thanks

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#### #12

Joined Nov 30, 2010
18,222
I recently told someone that resistance is by definition, not reactive...and was corrected. I will be watching to see how much magnetic flux is required to measure resistance.

#### wayneh

Joined Sep 9, 2010
17,152
According to Wikipedia:

Inductors have resistance inherent in the metal conductor, quoted as DCR in datasheets. This metallic resistance is small for small inductance values (typically below 1 Ω). The DC resistance is an important parameter in switch-mode power supply design. It can be modeled as a resistor in series with the inductor, therefore often leading to the DC resistance being referred to as the ESR. Though this is not precisely correct usage, the unimportant elements of ESR are often neglected in circuit discussion, since it is rare that all elements of ESR are significant to a particular application.
An inductor using a core to increase inductance will have losses such as hysteresis and eddy current losses in the core. At high frequencies there are also additional losses in the windings due to proximity and skin effect. These are in addition to wire resistance, and lead to a higher ESR.

So I guess there are contributions to ESR above and beyond the simple DC resistance. Though these contributions change with frequency, they are not part of the inductance, the frequency-domain reactance.

• Schniz2 and #12

#### oldtech33709

Joined Sep 24, 2011
26
ESR is a common spec for switch mode capacitors, not so much inductors. I think your looking for DCR, or the dc resistance of the coil.

Thread Starter

#### Schniz2

Joined Apr 15, 2010
22

An inductor using a core to increase inductance will have losses such as hysteresis and eddy current losses in the core. At high frequencies there are also additional losses in the windings due to proximity and skin effect. These are in addition to wire resistance, and lead to a higher ESR.

So I guess there are contributions to ESR above and beyond the simple DC resistance. Though these contributions change with frequency, they are not part of the inductance, the frequency-domain reactance.
As wayney said above, the ESR value is a lumped value of the resistance including the skin effect, eddy currents, core losses etc. I was after the resistance the current will see at a certain frequency because i have to design a controller and the system transfer function includes the ESR of the inductor.
Maybe 20kHz is not high enough for the value to increase much beyond the DC resistance... if it is... how can i measure the ESR?

#### wayneh

Joined Sep 9, 2010
17,152
... how can i measure the ESR?
If I was a EE, I'd have the proper answer. As a chemical engineer, my answer is to measure heat production. Or, maybe you can perform an energy balance around the device and calculate heat by difference.

#### jt6245

Joined Feb 18, 2011
21
Maxwell bridge and Hay bridge can measure inductor and its ESR. Maxwell bridge is suitable for inductor with Q<10,and Hay bridge is suitable for Q>10.
Note Q is changing with frequency,for Q=reactance/ESR (reactance change with frequency).
You may look at this website or other for information of the Bridge.

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#### jt6245

Joined Feb 18, 2011
21
Your method to find inductance is wrong. Due to angle change,(magnitude of voltage R +magnitude of voltage inductor ) >magnitude of input voltage.

#### steveb

Joined Jul 3, 2008
2,436
If I was a EE, I'd have the proper answer. As a chemical engineer, my answer is to measure heat production. Or, maybe you can perform an energy balance around the device and calculate heat by difference.
Sometimes methods like this are very effective and EEs don't even consider them. A calorimeter setup has helped me more than once. Good comment!

#### wayneh

Joined Sep 9, 2010
17,152
Sometimes methods like this are very effective and EEs don't even consider them. A calorimeter setup has helped me more than once. Good comment!
Yup, when you can't compete in the game you're playing, change the game.

#### DickCappels

Joined Aug 21, 2008
7,441
Take your ohmmeter and measure the resistance.
Alternatively, for low frequencies look up the resistance of the wire, the mean length of turn for the coil form you are using, and using the number of turns, calculate the resistance. Or, use the actual wire length for the resistance calculation.

For higher frequencies or other cases in which core loss is a factor, find the Q of the inductor by using an inductance meter or bridge at the frequency of interest.

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