A Post Worth Keeping: VoltSecond on Chokes

May 08, 2004 Ver -

Minor format updates 23 Jul 2024

Question from Russ57 on May 07, 2004 at 12:49:35:

Anyhow, what is the difference between a choke that is speced only for use in a cap input supply as opposed to one also speced for choke input supply. And would it be correct to assume that a choke used in a choke input supply would have to handle a larger AC current than one with a cap input supply.

Reply Posted by:    VoltSecond on May 08, 2004 at 00:45:30    Link to Original Post about chokes

Choke me in the shallow water before I get too deep. . .(sorry Edie)

Yes, a choke used in a choke input supply needs to be designed differently than a choke designed for use in a capacitor input supply.

Yes this is because the inductor in the choke input supply has to handle a larger AC current. However, please note that a choke designed for use in a choke input supply will work fine in a capacitor input supply.

On to "WHY."

Warning: "Why" has been a dangerous question around me lately.

1. First a short discussion about "Q".

Core loss can be modeled with a resistor in parallel with the inductor. This resistance value doesn't change very fast with voltage or with frequency, so this model isn't too bad as electrical models go. This core loss resistance (R_parallel) is usually, but not always, the dominant factor in the Q of an inductor.

"Q" (Q_total ) varies a lot with frequency. This is because "Q" is a comparison of XL to the losses of the inductor at one single frequency.

        XL             = j * 2 * PI * F * L
        Q_parallel  = R_parallel / XL
        Q_series    = XL / R_series
        Q_total      = 1/ (1/ Q_parallel + 1/ Q_series)

If the losses stay constant with frequency, the Q_parallel will halve every time the frequency doubles and the Q_series with double every time the frequency doubles.

if the core loss resistance is a linear 100 kohm with both frequency and drive and the inductance is 100 H, then from 159 Hz on up (ignoring other parasitics), the inductor looks like a 100 k resistor, not a 100 H inductor.  ( 2 pi 159Hz * 100 H = 99.9 kohm )

Why bring "Q" up? Because we don't always get 100 times the times the noise attenuation in an LC filter if the frequency goes up a factor of 10. First is because of the core loss (Q_parallel) resistance removes the pole (attenuation) from the inductor. Second is because of the ESR of the capacitor will eventually remove the pole (attenuation) of the capacitor. (5 ohms ESR in series with 100uF gives a zero at 318Hz.)  Adding the R_parallel drop in filter attenuation to the drop in attenuation from the ESR of the capacitor, we may not get any extra attenuation if the frequency goes up a factor of 10.

Caution: If you compare "Q"s of two inductors, make sure you compare them

A. At the same frequency and drive level,
B. That you know the dc resistance of the inductor and
C. That you are comparing them at least at 1/5 the self resonant frequency (SRF.) SRF is an often misused figure of merit used in describing the capacitance of an inductor.

Now for more bad news:

Once we add the parasitic capacitance of the inductor and the parasitic inductance of the capacitor into the attenuation calculations, at really high frequencies we don't get any noise attenuation at all from a single LC filter!

 **** Now lets divide low frequency chokes (< 50 kHz) into four categories:****

2. Linear Chokes.

In these chokes you really only care about peak current when calculating the inductance. The DC inductance and the AC inductance of these chokes are essentially the same. When this happens it is easy to calculate volt * seconds from

        v * sec = L * I dc + E * T (note A)

Note A:

E * T is the integral of voltage over time for one half cycle of the voltage across the inductor and is measured between the zero voltage crossings across the inductor from the applied signal. E*T simplifies to just "voltage above zero * the time above zero" for a symmetric square wave. Sinewaves and other waveshapes involve a bit more math in calculating E * T.

Also note that:

        Energy in a linear inductor = 1/2 L * I^2
        Energy in a linear capacitor = 1/2 C * V^2

2.1. High ac ripple

With high ripple current you care about core loss because it can cause temperature rise problems. An example of a linear choke with high ac ripple current would be a plate or grid choke used in a Parafeed or SET amplifier. Another example would be a choke input power supply.

2.2 Low ac ripple

With low ripple current you don't care about core losses because of heating, but you still may care about "Q." So even with low ripple currents, there may be a need for low core losses.

An example of low ac ripple current would be an inductor in a filter network that must operate linearly when exposed to infrequent voltage spikes.

3 Non-linear chokes

With non-linear chokes you still care about the peak current, but specifying how you use the choke and the inductance with current gets to be more of a challenge. This is because the inductance MAY change with current and/or with frequency. This makes calculating the volt * seconds more difficult.

3.1. High AC ripple

With high ripple current you care about core loss because it can cause temperature rise problems.

This would be and example of a choke input filter. Here if the inductance is higher at low currents that at maximum current we can get better regulation in a smaller package because of the "swing" in the choke's inductance. "Swinging Chokes" are a really nifty way to get good regulation over a wide current swing in a choke input filter.

Please note that you don't want to oversize the current rating for an inductor in a choke input filter. This is because if the choke does not saturate at power up, the output voltage of most choke input filters will overshoot to twice the normal DC regulation point. This is because the inductor stores just as much energy as it puts into the capacitor during the initial turn on. Now when it releases this stored energy, it dumps it into the capacitor.

The capacitor rings up to twice the input voltage (4 times the normal energy storage), not 0.7 times than the normal input voltage (2 times the normal energy storage.) This is because the input side (transformer side) of the inductor is effectively at the normal voltage regulation point. This allows the inductor to draws more the energy from the power input by adding the energy drawn from the power input to what it has stored in it as it charges the output capacitor.

3.2 Low AC ripple

Again, with low ripple current you don't care about core loss because of heating, but you may care about "Q" So even with low ripple currents, there may be a need for low core losses.

This would be a choke intended for CLC use; however, a high AC ripple choke would work great in CLC filter us.

4. (accidentally deleted)

5. Why do we care about volt * seconds?

Because

        Gauss = 10^8 * volt * seconds/ (N * Ac (in cm^2) )

Gauss is the units used to define where a core saturates and the amount of core loss in a core. ( I prefer Gauss over tesla, mostly because Gauss and inches are the units from which I I learned how to magnetics. )

6. Beware of the SRF specification!

Simply

        SRF = 1/[ 2 * PI * sqrt (L_core + C_coil).

What can go wrong with that?

Well, the inductance of some cores drop off rapidly with frequency. If we compare two inductors, A and B, with the same parasitic capacitance:

A is an above average inductor whose inductance does not drop off with frequency (the better inductor)
B is a typical inductor whose inductance has dropped a factor of 100 at the SRF.

The better inductor (A) has an SRF 10 times worse (LOWER) than the typical inductor. I bet marketing and purchasing really likes that (B) part! But the engineer doesn't.  ( This is a real problem I have fought.)

7. Into the deep water (info from Paul and Lowell's articles):

In a piece of magnetics :

        E = L di/dt + I dL/dt

Usually in transformers and inductors we usually ignore the “I dL/dt” and just use:

        E = L di/dt

The dropped “I dL/dt” part comes in handy for motors, speakers and such. 

Which can be rewritten as:

        E dt = L di

        E dt is the voltage integrated over time, or Volt * seconds.

Volt * seconds are useful because:

        Ac^2 * Aw/ MTL = pd^2 * { (LI)^2/ DCR }/[ Kc * (Ur * H)^2 * (Ap/ Aw) ]

Ac = Area of iron in the core
Aw = Available area for copper in the core
MTL = mean turn length (average length of wire for 1 turn)

Ac^2 * Aw/MTL is also known as the “inches to the fifth” of the magnetic core. Yes I know in a modern world this should be “cm to the fifth.” Most of my core catalogs have all the values in inches. I don’t like the format of the newer web catalogs with the dimensions in cm. The format they are in is slowly improving. Since I'm not in the magnetics business anymore, I'm in no hurry to correct the error in my ways.

“pd^2” = resistance per length * diameter of wire^2. I just use .013 for round copper wire, double film with “p” in mOhm/ft and “d” in inches. #16 round copper double film has a pd^2 of .01193, #24 = .01323, #36 = .01646. When you set up the core tables, the inches to the fifth for each core usually changes 50% to 300% between core sizes. If you know you will be using fine wire, use .016 for pd^2. If you know you will be using heavy wire, use .012 for pd^2.

L = inductance under bias of the reference winding
I = bias current used for the reference winding inductance test point.
DCR = DC resistance of the reference winding

“Kc” = design constant = 49.95E-12 (50E-12) for Ac in square inches, Aw in square inches, MTL in inches, L in henries, I in amps, DCR in ohms and Ur*H in Gauss (peak).

“Kc” = design constant = 472E-15 for Ac in square cm, Aw in square cm, MTL in cm, L in henries, I in amps, DCR in ohms and Ur*H in Gauss (peak).

Ur = permeability under bias for the core material
H = oersteds the Ur data point was taken at, Ur * H = Gauss. This Gauss will not line up with the BH curve because permeability is complex. This Gauss will line up with what the LCR meter will read with DC bias, which is what we usually want anyway.

Ap/Aw = ratio of area the reference winding occupies over the available copper area in the core.

For transformers:

        Ac^2 * Aw/ MTL = pd^2 * { (volt * seconds)^2/ DCR }/[ Kc * (Gauss peak)^2 * (Ap/ Aw) ]

If you have a transformer with DC bias, then the  volt * seconds = L*I + the average voltage for one half cycle of the input voltage at the lowest frequency.

Once you have your core picked out, the turns on the reference winding are given by:

        N = Kn * (L* I)/[ (Ur* H) * Ac ] = Kn * volt * seconds/( Gauss * Ac)

For Ac in in^2, Kn = 15.5E6.
For Ac in cm^2, Kn = 100E6 = 1*10^8

If you are designing an inductor:

        Ur = Ku * L * lm/( Ac * N^2) Ur = relative permeability.

For lm in inches, Ku = 31.3E6.
For lm in cm, Ku = 79.58E6.

Now if you are designing a transformer instead of an inductor, you can use these same equations referenced to the primary winding, but just set (Ap/Aw) = approximately 45%.

8. Now if you think I've given you enough info to design a choke, well. . .not really

There are many other things to consider like

    desirable and non-desirable material non-linearity (in both Ur and core loss ),
    Q,
    total core loss,
    total copper loss,
    material constraints,
    manufacturing constraints,
    multiple parasitic capacitances,
    eddy current losses,
    gap losses,
    fringing effects,
    shielding,
    corona,
    temperature rise,
    lead setting method and strength,
    ac inductance changes with temperature/ frequency/ drive,
    vibration generated in the inductor shaking the circuit,
    effects of vibration on the inductor changing the inductance or adding stray voltages,
    core loss changes with temperature/ frequency/ drive,
    voltage breakdown,
    moisture sensitivity,
    hydrolytic stability (related to moisture sensitivity),
    regulation,
    insertion loss,
    characteristic impedance,
    magnetostriction,
    solvent/ dust resistance of the finished coil,
    flammability
    safety aspects etc. etc.

Mike LaFevre liked this post enough he put it on his Magnequest Technical Reference page.
https://web.archive.org/web/20071013095350/http://magnequest.com/mq_magnetics.htm