CHOKES - PAGE 1.
Updated 2017.
A. What is a choke? General information about inductance and filter chokes.
B. Simplest choke measurement.
Fig 1. Schematic for measuring choke without Idc.
C. MEASURE CHOKE EXAMPLE :-
Steps 1 to 10.
D. Iron cored inductance and permeability µ and µe.
E. Testing chokes for CLC with Idc.
Fig 2. Schematic for testing choke with Idc.
Steps 1 to 7.
F. LF resonance of CLC filters.
Fig. F response of low pass LC filter.
G. Alternative CRCRC to CLC
H. Bypassing choke with R+C for damped 100Hz resonance.
I. Hanna's method of choke design, RDH4.
Table 1, wire sizes for Grade 2 winding wire.
Table 2, choke details based on T25mm x S25mm E&I.
Steps 1 to 9.
K. Winding chokes.
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For chokes in PSU with CLC filters with high Idc, low Vac across L, you are at Chokes 1
For chokes in PSU with LC filters with high Idc and high Vac across L, go to Chokes 2
For chokes for high or low Idc feed to anode with high AF across L, go to Chokes 3

(A) What is a "Choke"?

I do not know why anyone named a coil of wire to be a "choke", but very soon after
electricity was put to use in many ways by 1900, people were winding coils of insulated
copper wire around iron to make an inductance to inhibit the flow of ac, alternating
current, Iac, or to "choke the flow" of ac, alternating current.
At early time in our knowledge of electronics, inductance was found to have 1,001
uses in coils and transformers for power transmission, telegraph and phone
communications and radio transmitting and reception. Inductance is a good filter
element to reduce unwanted Iac flow between point A and B in a circuit. The right
quantity of inductance with low wire resistance and low shunt capacitance makes a
very simple rugged filter element. But the choice for a choke depends on the application,
size, weight, cost and perhaps and several other factors.

The mathematics I have here is most basic and is free of quantum physics which
surround behavior of inductors. There is enough necessary maths to enable most people
wanting to make a good choke in a workshop. Definitions of Inductance do exist
elsewhere on the Internet, and most people could be completely bamboozled by
mathematics.

Basically, if there is change of current through a coil of enamelled wire there will be a
change of magnetic field produced. The field has direction just as the north - south
direction of Earth's magnetic field "poles". But with a coil subject to applied Vac and with
Iac, the field direction changes with direction of current. The applied energy is described
as Magnetic Motive Force, MMF, expressed as the current x turns, or At. The MMF, is
often stated simply as F, but not confused with F for frequency, so context is king, OK.
The F causes production of a magnetic field. For Idc, the field is constant, and does not
cause any opposition to Idc flow in wire.
Where there is Vac applied across a coil, there is Iac and a changing magnetic field
which changes direction and magnitude.
This change of Vac produces an "electro motive force", EMF, which opposes the
change in the flow of the Iac.
This phenomenon is difficult to understand.

Where there is only Idc in the coil, there is a fixed magnetic field ( like Earth's ).
Consider a typical iron cored filter choke coil with 2,000turns and wire resistance = 50r.
With +5Vdc across coil, there is 0.1Adc. This coil acts like a 50r resistance where t
here is only 0.1Adc flow. If the Vdc is instantly switched to -5Vdc, there is no instant
change of current, but I change will occur slowly, until current = 0.1Adc in the opposite
direction. The magnetic properties of the coil are opposing the current change when
rapid change occurs. If a 5Vrms x 100Hz sine wave is applied across this coil, the Ia
change may be found to be only 2.3mArms. The coil behaves like a resistance with
R = 5V / 0.0023A = 2,174r. If the sine wave is at 50Hz, the Iac = 0.0046MArms,
and the apparent resistance has changed to 1,087r. Thus the choke resistance varies
with to frequency of applied V. The coil inductance, L, has the property of a reactance,
XL, for which the unit is the ohm, or r.
XL = 2 x pye x Frequency x L, where pye is a constant for all equations = 22 / 7 = 3.14286,
Frequency is in Hertz, Hz, ie, wave cycles per second,
and L is Henry, the unit of inductance named after Joseph Henry, an American scientist
who died in 1879.

With Iac and Iac, any conductor creates a magnetic field around itself. The field around a
piece of wire is fairly weak, but where many turns are wound into a coil, the magnetic field
lines around each wire combine together to become much stronger, and a magnetic field
has a direction along centre line of coil then spreading out at one end of coil and returning
to the other end.
An invisible magnetic loop is formed. It can be most clearly seen where an electro magnet
is sprinkled with iron filings. There is no pattern to the filings with no Idc. But Idc is switched
on, the filings immediately form lines which show where the lines of magnetic field exist.

When Vac is applied across a coil, there is Iac flow and the field changes with frequency
and it opposes the flow of Iac where the frequency is high enough. If iron filings are sprinkled
on a coil with say 50Hz current, they are less likely to show the pattern of lines because the
direction of field changes 50 times a second and the filings jump about a fair bit, and do not
illustrate what is really going on. With 5Vrms x 100Hz applied across the coil with 2,000t,
the field strength is much less than there was with 5Vc across the coil.
It is the Change of applied Voltage which changes the magnetic field which creates
opposition to the current flow. The opposition to current flow when Vac is applied to a coil.
If the frequency was 0.001Hz, barely above 0.0Hz, there is not much opposition to current flow.
But at 100Hz, there may be a lot of opposition, and much less Iac flows, and at 10kHz,
almost no Iac flow. A piece of wire 25mm long has a very small amount of inductance.
But the reactance XL at 1GHz may be so high it is difficult to get Iac to flow. So all modern
circuitry operating at such high F must have extremely short connecting wires and small
circuits within ICs, and any understanding of what exactly happens in an IC can become
a mystery. Magnetism is at work, among other things.

Electro-magnets are used in many industrial applications. In early loudspeakers before
permanent magnets were able to be made, the anode Idc supply current was fed through a
field coil to generate a strong magnetic field in an annular gap between a rod of iron and a
surrounding plate. The cylindrical voice coil worked with the dc magnetic field across the gap
to produce motion to create sound waves.The speaker was a kind of electric motor.
The speaker electro magnet was known as a "field coil" and had thousands of turns of fine
wire carrying say 50mAdc to a 6V6 in an old AM radio. The 50mAdc in say 5,000turns gave
F = 0.05A x 5,000t = 250At, and the iron of the speaker is arranged to make an electro
magnet with iron path length of about say 200mm, but including a gap of say 2mm in which
the magnetic field intensity may be a fixed 1.2Tesla in one direction.
In this annular gap, the voice coil attached cone can move with the high Iac and low Vac
producing a force to make cone move.

This old fashioned method of building an early electromagnetic speaker was invented in
1930s, and the coil to produce the intense magnetic field for voice coil was called a
"field coil" and was used to filter the B+ produced by HT winding and diodes and caps
to allow hum-free sound from the radio.
During early 1930s, the same basic idea of using many turns of wire on a core of iron was
used in chokes to filter out Vac content while allowing easy flow of Idc. Many old radios
had a field coil which had L = maybe 5H, and filter caps for CLC were typically 8uF or 16uF,
and expensive, and unreliable. A modern electrolytic with same size as 1935 16uF x 450V
rated may now have 470uF x 450V, and is much cheaper, and more reliable.

Many tubed amplifiers still use CLC filtering for their B+ anode supplies to reduce the
Vac at B+ rails to extremely low levels to allow tube operation from a supply that is like a
large 400Vdc battery, but of course the 400Vdc cannot be maintained when mains power
is turned off.

The term "impedance" is also used for a choke but usually it should be called reactance
because wire resistance and winding self capacitance have negligible effect on operation
and calculations for the intended use at 50Hz or 100Hz in PSU, or where frequencies are
between 14Hz and 50kHz for choke feed for Idc to anodes. Impedance is the name used
for networks of two or more L, C or R elements with at least one being L or C, and with all
being relevant to the operation.

A filter choke in PSU have L reactance XL, plus wire resistance Rw. The Rw is often ignored
in some calculations for Vac but is relevant for Idc calculations where the Vdc across Rw is
important to design the Vdc supply for the whole circuit to work. The LCR model of a coil is
the pure L + Re in series, with its shunt C across the L+R.

A choke for CLC may have 3.4H and have Rw = 50r. At 14Hz, XL = 6.28 x 14 x 3.4 = 298r.
The impedance includes Rw 50r and.
ZL = sq.rt ( XL squared + Rw squared ) = sq.rt ( 89,358 + 2,500 ) = 303r. So the 50r has
very little contribution to the reactance XL. For series R+L, Rw makes very little difference
to the total Z where XL > 10 x Rw.

For all series L + R,
impedance Z ( L+R ) = Square root of ( Rw squared + XL squared ) ohms, r.

For all parallel L // R,
impedance Z ( L // R ) = 1 / sq.rt ( 1 / R squared + 1 / ZL squared ) ohms, r.

Most electronics behavior is governed by fairly simple mathematics, so remember this
phenomenon, and remember to leave a lot of your silly common-sense behind when you
enter the world of electronics, or you will be lost.
Unfortunately, the simple electronics can turn into a huge nightmare of complexity when
more than 3 LCR elements are connected. I found that all the free software to enable
calculation of passive LCR networks vanished from the Internet to be replaced by programs
you must pay for. There are a few CAD programs for free which I found always far too
difficult to use because the NERDS who wrote the codes have zero ability to teach
anyone else anything. The Help offered by many apps and programs turns out to be

Where possible, Rw should be minimized to avoid unwanted Vdc drop across choke Rw
and to avoid heat dissipation.

(B) Simplest choke measurement without Idc :-
Fig 1.

Fig 1 shows an inductance being measured. Similar set up can also be used for
measuring capacitance values. The test circuit may be set up on panel of plywood
say 200mm square, with 12mm x 4 gauge brass cupboard screws for connection
points and bare 1mm dia Cu wire used for links. Rotary wafer switches can be
mounted on a number of screw heads or on a metal panel near one edge of board.

Tools needed :-
A good signal generator, able to make 2Hz to 200kHz, sine wave, square wave, with
accurate F indication. Possible frequency meter if signal gene has a dial with poor
calibration. Oscilloscope ( CRO ) with bandwidth up to at least 1MHz. Many are 15MHz,
dual trace, but single trace is OK.
40W audio amp, bandwidth 7Hz to 50kHz, -3dB points, to give 15Vrms at least, Rout < 1r0.
Vac meter with multi ranges and bandwidth of 5Hz to 200kHz and giving Vrms.

Most DMM are useless for anything below 10Hz and above 2kHz and have Cin = 1nF
which loads the choke so once you have measured the Vac at 1kHz to be say 10Vrms at
VL, you know what amp Vac will be for say 10Hz to 30kHz. Do not clip Vac meter across
choke.
The measurements are all made by applying Vac across choke from low Z Vac source,
and measuring Iac flow in either 10r0 or 100r.
The Vac across 10r0 or 100r will mostly be much lower than Vac from amp.

Solder, patience, persistence, and the will to understand and to never assume anything.
Note book and pencil.
Computer, i-pad, mobile phone and keyboard are NOT NEEDED, or damn well
wanted anywhere near any man trying to understand basic electronics without feeling
bored, or that he should be doing something else, which afflicts over 50% of everyone.

R1 is simple toggle switch, use a rugged one. It allows choice of current sensing R
of 10r or 100r and if the choke has short circuit or is low L air core type, the amp has
lowest possible load of 10r0 so amp should never be damaged, and I know of course
that where something can be Pharqued Arpe, it will be, if idiots are present.

Some zealous folks would want dual trace CRO and set it up to view VL to 0V on chan A
and Vac across R1+2 on chan B.
This is a super good idea, you NEED to know if any THD appears which may render
measurements to be bullshit.

The CRO allows anyone to see the distortion in an iron cored choke at VI.
THD from sig gene and amp should be < 0.5% and usually hard to see on CRO, but you
will see 5% easily if the choke begins to saturate with LF Vac.

If air cored inductances are measured, they should not produce any THD,

The signal generator should give the same constant Vo for say 2Hz to 200kHz but
F and level is adjustable. Sig gen Rout should be < 600r so that connection to a small
power amp input does not have any effect on sig gene Vo level. Many "Signal generators"
or "Function generators" have "decade" ranges say 2Hz to 20Hz, 20Hz to 200Hz and so
on up to 200kHz which an audio tech uses to test audio gear. The better and more
expensive but fragile function generators have a top frequency of 2MHz, with dc
offset, sine wave, square wave, triangular wave, maybe saw tooth wave, FM and
AM modulation etc. But for this test you only need sine waves.

This test schematic does not include ability to measure with Idc flow in choke.
Those of you who insist on Idc being present, make a variable constant current
source between +40Vdc rail so that its impedance and capacitance ads no parasitic
R or C that spoils the measurement of L measured. The Idc may cause choke to
saturate but that is OK, you will measure that, but the CCS will remain invisible.

The amp used can be any generic solid state audio amp capable of 40W to 8r0
= 17.88Vrms max, but most audio power amps have F range of say 5Hz to 30kHz
at max Po and maybe slightly more F at 1/2 Po for 12.6Vrms. Testing with amp
level set for 10.0Vrms at 1kHz is good start.

L values could be between 0.1mH and 500H.

(C) MEASURE CHOKE EXAMPLE :-

Wasteless pattern E+I choke, T25mm x S25mm, Core material quality is unknown.
Its age indicates if could have been made in 1960 with NOSS E+I.
Turns are unknown, I are are butted to E with small unknown air gap.
Random winding pattern without layers and insulation.
Magnetic length and average turn length for this core size = 138mm.

(1) The wire size looks to be approximately 0.42mm oa dia using micrometer, so Cu
dia = 0.35mm Cu dia. Iron ML = 139mm, average turn length TL = 139mm.
Rw measures = 47r.
Now Rw = N turns x ML mm ( 44,000 x Cu dia squared ).
Thus N turns = Rw x ( 44,000 x Cu dia squared ) / TLmm
= 47r x ( 44,000 x 0.35mm x 0.35mm ) / 138mm = 1,835t.

Check if this is possible. For T25mm material, bobbin winding area available for wire
= 33mm x 10mm = 330sq.mm.
If oa dia wire = 0.42mm, then max N can be 330sq.mm / 0.42mm squared = 1,872.
For random winding, the turns are always less than theoretical so N could be 1,835t,
depending on exact size of wire. Assume N =1,800t.

(2) Set S1 for R1 = 10r0. Unknown choke is connected to VL and VI points.

(3) Set signal gene to give 10.0Vrms at VL to 0V at 1kHz from audio amp. Measure VI across
10r0 and you may 0.0062Vrms, tiny, and maybe not correct, so switch for 100r,
Then you might measure 0.062Vrms and Iac = 0.062 / 100r = 0.62mArms.

XL = 10.0V / 0.62mA = 16.1k.
L = XL / ( 6.28 x F ) = 16,100r / ( 6.28 x 1,000Hz ) = 2.57H. Use of higher or lower Vac may give
slightly different L result.

(4) Repeat the measurements with same VA, but at 500Hz, 200Hz, 100Hz, 50Hz, and 25Hz
if possible. THD may begin to exceed 10% at LF.

The choke is to be used for CLC filter if possible. Therefore its properties at 100Hz are important.

Measurement at 100Hz with VL = 10.0Vac could give 0.318Vac at 100r, so Iac = 3.18mArms.
XL = 10V / 0.00318 = 3,140r.
L = XL / ( 6.28 x F ) = 3,140r / ( 6.28 x 100Hz ) = 5.0H.
Don't be surprise to find L at 1kHz is a bit less at 100Hz. This is because even with an air gap,
the L value varies because the iron µ value varies with F, and so does µe, but the the L varies
much more without an air gap than with an air gap.

(5) What is the ue for the choke?
"µe" is the effective core permeability for the F and Vac amplitude used for the test.
Calculate µe at 100Hz.
Inductance for coil with E+I core or C-core =
L = 1.26 x N squared x Afe x µe / ( 1,000,000,000 x iron ML )
1.26 and 1,000,000,000 are constants for metric measurements, L in Henry, N = turns,
Afe = Tmm x Smm of core, ML in mm.

Therefore µe = L x 1,000,000,000 x ML / ( 1.26 x N squared x Afe )
= 5.0H x 1,000,000,000 x 139mm / ( 1.26 x 1,800t x 1,800t x 25mm x 25mm ) = 272.

Now this µe is much less than the max possible µ with all E+I maximally intermeshed
which could be between 1,500 for worst old iron and 10,000 for real good GOSS.
Adding Idc through the winding magnetises the core but because there is an air gap the
Bdc change from no Idc to a lot of Idc may not change the µe or measured XL very much.

As air gap increases µe reduces and so does L. Idc makes less difference to L provided
the core is not saturated by Idc and the applied Vac does not cause core to saturate.

It is planned to use the choke with Bdc up to maybe 0.8Tesla.
For this choke, if Idc = 150mAdc for 2 output tubes,

Bdc = 12.6 x N x Idc x µe / ( 10,000 x ML )
where Bdc is Tesla, 12.6 and 10,000 are
constants, N is turns, Idc in Amps dc, µe is calculated number that is thought to be true,
ML is iron magnetic length in mm.

Bdc = 12.6 x 1,800t x 0.15A x 272 / ( 10,000 x 139 ) = 0.67Tesla.
This tells you that you could have more Idc, but core is not saturated.
Core might saturate at 1.1Tesla. The Bac possible = 1.1T - 0.67T
= 0.43Tesla.

Now N = Vrms x 226,000 / ( Afe x Bac x F )
so Vrms max = max Bac x Afe x N x F / 226,000
For this choke, max Vrms at 100Hz = 0.43T x 625sq.mm x 1,800t x 100Hz / ( 226,000 )
= 214Vrms.
At this Vac, the choke should begin to saturate, but the test gear cannot supply
214Vrms to find Fsat, from which we might more accurately know the max possible Bac.
Because there is no Idc, max Bac might be 1.1T to max Vac could be 547Vrms.
If the F was reduced to 10Hz, the Vac for 1.1T would be 54.7Vac, no Idc.
With Idc, Vac max may be 21.3Vrms.
It becomes difficult to work out exact properties any more than I show here but you can
tell if the choke is usable, or if it has a fault like a shorted turn.

If the above choke is used in CLC filter with C1 = 47uF where Vac at C1
= 10.3Vrms x 100Hz, and if C2 = 220uF, and if L = 5H, the XL at 100Hz = 3,140r.
XC2 220uF at 100Hz = 159,000 / ( 220uF x 100Hz ) = 7.2r.
Vr ripple voltage at 100Hz at C2 can be calculated = Vac at C1 x XC2 / XL at 100Hz
= 10.3Vrms x 7.2r / 3,140r = 0.024Vrms.

This indicates quite good attenuation factor = Vo / Vin = 0.024V / 10.3V
= 0.00233, ie, 1 / 429, or - 52dB attenuation.

The full properties of this choke may be found where it is working in a PSU.
The air gap might be adjusted down a little to increase µe for L = 7H and that
would increase attenuation factor to 1 / 600. The resonant Fo for 7H and 220uF
= 5,035 / sq.rt ( L mH x CuF ) where Fo is frequency Hz, and 5,035 is a constant.
Fo = 5,035 / ( 7,000mH x 220uF ) = 4.0Hz which is nicely lower than the AF band
official beginning at 20Hz.

(6) All chokes have some capacitance between layers of windings which sum to
form the "self capacitance" of the winding when measured from one end of the
winding to the other. There is a small amount of C between adjacent turns of wire
which adds up to be significant. For PSU choke in above test, self C < 300pF.
It forms a parallel resonant circuit with the L. To find Fo with above test circuit will
be difficult because the Q of the LC resonance is low, maybe 1.0, and the L
value may have halved at somewhere above 1kHz, and unless you know what
L is as F rises then the Fo for self resonance is impossible to calculate.
But you should measure XL rises with increasing F above say 30Hz where it
may be lowest at 1.32k to 32k at 1kHz and 60k at 5kHz and then the ZL
curve levels and reduces above 20kHz. The reduction of XL is due to the
shunt C of choke plus oscilloscope probe C which could be 100pF.

If a graph is drawn for XL from say 10Hz to 40kHz, you may see a curve like the
Sydney Harbour Bridge.
The XL for 5H at 10Hz = 314r, 3,140r for 100Hz, maybe 16k at 1kHz, and somewhere
above 1kHz the XL will begin to reduce at a rate of -6dB per octave and that is effect
of shunt C between winding ends. The XL continues to rise, but the XC becomes a
falling value as F is increased. The L and C form a parallel resonant L+C circuit where
the maximum XL occurs at the top of the bridge curve. The attenuation rate of -6dB
per octave is at F above the maximum XL.

If shunt C = 200pF, then at 40kHz, XC = 19.8k, and 10V across this gives 0.5mA
so you would see 0.05Vac across 100r, and at 80kHz if you could have 80kHz
it would be 0.1Vac where XC = 10k.

Theoretical Fo for resonance for Cshunt and L cannot be predicted because L reduces
as F rises while C remains fixed. But if the choke is to be used to feed Idc to an anode
to give a high impedance load of at least 2k0 for most AF then the choke should be OK.

Fo for all LC =5,035 / sq.rt ( L x C ), where Fo is in Hz, 5,035 is constant for all equations,
L = milli-Henry mH, C = uF.

(7). But whatever Csh exists, it is able to pass some of the diode HF switching noise pulses
which are a bunch of HF oscillations above 50kHz occurring 100Hz rate. These often
manage to get into audio path and are clearly seen on CRO at amp output with amplitude
up to 10mVpk. It makes a harsh noise if its amplified. But the choke is often not the real cause.
The noise may get into audio path via 0V path because the HF switching pulses can travel
easily in low impedance 0V rail. The connections of diodes and HT secs must be done so
Vac from HT winding is applied to reservoir C without including any length of 0V rail.
Star earthing also helps.

I found using 0.47uF x 630V polyester; across C1 and C2 electros of CLC helped and
0.05uF 1,000V across HT windings. Keep 0V paths correctly short, and keep input circuits
and NFB wires away from PSU. DO NOT use the chassis as the 0V rail.

When ALL noise of any kind at amp Vo = 0.25mV with input shorted to 0V with RCA
shorting plug, you have a low noise power amp. If an amp makes 28Vrms max for 100W to
8r0, SNR is considered = 100dB, good, by any standard, but where Vo = 1Vrms, SNR
= 72dB, also excellent. I have measured and fixed dozens of noisy amps.

(8) For choke measured above, it may be impossible to use it for a choke input supply
for where you have HT winding with diodes feeding choke then a reservoir C.
If B+ was say +400V, the HT Vac for LC input will be near to Vdc / 0.88. So for +400V,
you need Vac = 400 / 0.88 = 454Vac. The amplitude of 100Hz applied to choke =
about 0.45 x HT Vac = 0.45 x 454Vrms = 204Vrms.
Now if you want 150mAdc for LC input, then the L must be RLdc / 900 Henry for where
Idc = minimum, or in this case 15mAdc, 1/10 of the working Idc, So you must have a
bleeder R for 15mAdc = 27k rated for 10W. The L must be 27,000r / 900 = 30H, and the
5H above would be useless because it is only 5H.
Chokes 2 explains it further.

(9) What is max Idc for 5H choke above? Rw = 47r with 0.35mm Cu dia wire.
Acu = 0.096sq.mm.
If max current density = 3A / sq.mm, max Idc = 3 x 0.096 = 288mA.
This makes heat = Idc squared x R = 0.288 squared x 47r = 3.9W. BUT, the winding
would get hot, and the 288mAdc is far more than wanted and would cause core saturation
but would not fuse the winding within a minute.
If Idc = 150mAdc, then heat is 1W and core is happy. Current density = 1.56A / sq.mm = OK
With 150mAdc, Vdc across choke = 7.05Vdc = small % of B+ = OK.

(10) Air cored inductors have advantages for many AF and RF applications but it is difficult
to make large useful amounts of inductance without using iron cores. An air cored 10H filter
choke without iron core and with Rw = 50r may be 50 times larger than the iron core
choke and would be an expensive waste of copper.

For crossover filter chokes for speakers, attenuator networks in amplifiers, etc, air cored
chokes are often used because the amount of inductance required is usually less than 50mH
and they create no distortion, are fairly cheap to make, have constant L value for all levels
of Vac, and work from DC to RF, and there is never any saturation.

Some crossover coils used in series with bass speakers obstruct HF signals have
pre-moulded iron dust cores or a bar made of stacked laminations in a solenoid design
to increase L and keep winding R low. Usually the bar cored solenoid choke raises L by
a factor of only 4 above that for the same coil with no iron core.
Inductance is roughly proportional to number of turns squared, although for air cored L,
Wheeler's formula works well to calculate air core inductance. The size and shape of the
coil matters with air cored L. But if there is a centre hole big enough for a bar of lams using
some spare Is from a transformer, the L may increase by about 4 times. Using GOSS bar
keeps THD low, but rules for Bac apply.

It is always best to only use air cored L in series with bass speakers to exclude HF.
The Rw should always be less than 1/10 of the speaker impedance in its centre of
bandwidth, so if a 4r0 speaker has Z = 3r0, then a 2.4mH choke should have Rw > 0.3r,
for cut off = 200Hz.
Hi-end crossover coils are very large to minimize Rw losses. And very expensive.
But the size becomes lower as F rises for midrange drivers and tweeters so there is
no need for any iron in L for speaker crossovers.

Good speaker design follows all the rules about LCR theory.

Some of the larger air core crossover coils can have a bar core added to make a 4mH
choke into 16mH, which has XL = 10r0 at 100Hz, so they may be used for CLC in a
PSU.
So for CLC with 2 x 4,700uF plus 16mH, 100Hz attenuation factor = 0.035. This could be
for 2Adc for input tube heaters, or for a solid state PSU and Vr at C2 = 32mVac.
However, the 2Adc produces Bdc in bar, but ue is very low at say 4 because the air gap
is longer than iron ML, so the Bdc may not be very high.

For filter chokes in power supplies, we really only need to know what the inductance
will be at 100Hz, because rectifier ripple frequency = 2 x mains 50Hz UK, Europe,
Australia, and elsewhere. Any power supplies built in "50Hz" countries will work fine
where 60Hz mains exists in the USA. Some iron wound components such as power
transformers designed for 60Hz operation in USA may not work well when exported to
50Hz countries. I am Australian, and all my formulas in this site are based around 50Hz
mains and I use metric measurements unless stated otherwise.

The above test circuit may have its R values varied further as desired if your reasoning
is correct. Practice with measuring and calculating should train you to work precisely
without guessing or assuming one single thing. The dedicated technician avoids making
amplifiers riddled with noise or with a bad smoking habit.

The pure L or the C reactance has NO resistance and therefore current flow does not
dissipate any heat, and no work is done in the L or C. But where the Iac or Idc lows in
wire resistance in leads, heat is produced and heat Power = R x Irms squared, or
Power = Vac squared / R, in Watts.

Energy is transferred by the L or C and can be temporarily stored but not lost if the
L or C is perfect, ie, has low resistance wire or leads, and no power is lost on heating
and iron core due to hysteresis phenomena.
.
The energy in a choke becomes stored in its magnetization. Increasing Iac in choke
increases Vac across choke, and increases the magnetic field and energy store. Reducing
Iac in choke causes opposite V change direction across choke as magnetic stored energy is
capacitance properties because most people remain ignorant of such basic ideas and
thus cannot ever learn to properly design their amplifiers. Once a "hands on"
understanding of how L, C and R behave with AC signals, then other concepts become clear.
---------------------------------------------------------------------------------------------------------------------------
(D) The iron cored inductance.
The L value changes for applied Vac levels and frequency. For a pure sine wave Vac
applied across an iron cored inductor there are distortion currents generated in the iron
due to what is called hysteresis. Nobody seems to be able to explain EXACTLY what
hysteresis is, in terms normal ppl understand. Most blokes know what a hysterical shiela
is alright, a woman who is crying, laughing and machine gunning your ears with bullshit.

BUT, those who want know what hysteresis does need only examine the magnetic
properties of any mains transformer winding on a core with no air gap.
The current wave is ALWAYS 90 degrees behind the applied Vac across the coil and
the distortion in current waves is low with a small Vac for lo Bac of less than say 0.3Tesla.
But as Bac increases above 0.3T, the distortion becomes visible on a CRO and if Bac
= 1.4T, the distortion currents may have risen above the level of fundamental frequency,
so the the impedance of the coil reduces and core heats up because some of the input
V x I power is converted into heat. The core heating is due to "eddy currents", and to
reduces these to a minimum the lamination thickness must be reduced so GOSS
material is often never thicker than 0.35mm. See my Graph 3 and 4 at
powertranschokes.html.

So what we need to know about an iron cored L is its suitability for a position in a circuit
as PSU filter L in CLC network. High Z anode dc supply for a triode, etc.

Usually, maximum inductance is wanted without any core saturation of a choke or
transformer.

Chokes in tube amps are rarely ever without Idc flow. Most have Idc flow in one direction
only in one winding, but a few have Idc flow in opposite directions away from a CT in one
winding. Thus the working effective permeability, µe, is usually less than the maximum
possible µ for any given magnetic core material, and one or more "air gaps" are inserted
into the magnetic path length of the iron core.
The reduced µe gives less Idc caused magnetization, Bdc, while not saturating the iron,
and allowing additional magnetisation by Iac, Bac, and the sum of Bdc and Bac should
never exceed the maximum B quoted in data for the material.

Most iron-wound inductors found in chokes and OPT in tube audio amps use Grain
Oriented Silicon Steel, GOSS, aka Cold Rolled Silicon Steel, CRGO.

Toroid coils wound on GOSS cores have the highest µ up to 40,000.
They are useless for where any Idc flow is used, in chokes, SE or PP OPT.
But it is splendid material for a PT, providing the windings have woven insulation to
allow easy varnishing and the transformer is potted. Few are, so I never bought many.
It is difficult to add an air gap to a toroid to reduce its µ to say 4,000 for a PP OPT
or to 400 for a choke.

C-cores are exceptionally good for chokes and all OPT. Air gapping is very easy.
and maximum µ could be 15,000, and it is easily reduced to any smaller value by placing
non magnetic material into the two gaps between the two C that make up a C-core O shape.

GOSS C-cores with their two cuts polished are excellent for PT and give low losses and the
ZL curve shows that distortion currents are low at the onset of core saturation which is often
at 1.2T. Toroids and C-cores have the lowest eddy currents at mains frequencies so have
lowest loss of Watts / Kg.
C-cores made by Nicore.com are also excellent. But I have no idea
where small quantities may be purchased.

GOSS sheet can be cut into E and I shapes to make E+I cores. It is often 0.35mm thick.
The GOSS material favoured by ppl making tube gear is known as M6, and AK Steel in USA
The raw material for transformer cores comes in rolls of material, maybe 1M wide x 0.35mm
thick and the grain direction is along the length of the roll.
The E are stamped from the roll in pairs of E facing each other and two I come from the
material between the three E legs.
Thus grain direction is along each of 3 legs of E and along the I. But when assembled to
make E+I core, the magnetic "lines of force" run along each E leg easily but then flows at
degrees to get into E upright with difficulty, and if you consider the assembled E+I core,
the path length includes material with lower µ because of grain direction so the max µ for
E+I is usually never as high as for C-cores or a toroid.
And it seems this inherent character of E+I show that the ZL curves I have plotted for
GOSS show distortion currents increasing above about 0.5T, and the wound coil and core
has much steeply reducing ZL above 0.5T. But there is no need to worry about this until
Bac gets to 1.2T or maybe 1.5T, depending on the use and nature of E+I.
The E+I is thus OK for a PT or OPT if Bac = 1.2T if the load value for the winding is well
below the non loaded XL value at 1.2T.

Where the applied Vac produces Bac above 0.5Tesla the E+I core begins to saturate,
and up to 1.2T the pure inductance seems non linear but the core still works well enough
to be a high enough impedance if the load value is typically many times lower than XL
at 1.2T. Above 1.2T, the distortion currents in core become high enough to make the
Z ( RL // XL ) generate significant distortion in Vac across the RL // XL, and where this
is say 5% THD at say 1.2T, there cannot be any higher Vac applied.
For any Bac increase above say 1.2T, the peak Iac becomes rapidly higher and if Vac
is say doubled, the core would behave as a magnetic inductance up to 1.2T, but for 2.4T
the coil acts as a piece of wire, ie, the coil winding resistance.
I had customers who had bought CD players online from USA meant for 115Vac mains input.
They eagerly unpacked the item here in Australia and plugged it into our 240Vac mains and
within 1/2 a second the item was totally wrecked, because Vdc rails went to twice normal
value and then the mains transformer winding fused and then the mains fuse blew.
They were made more unhappy when I advised them the item was not fixable.

So it is important to know the properties of the iron being used for any project you have.
The iron values are both queer and vague, and the God Of Triodes did try to work out a
better deal with the God Of Steel, who is a terribly stubborn entity. You need to know
anything with turns around iron is a puzzle, but if you can deal with variable parameters
you will understand. So tell yourself, in a loud voice "Understand This Coil ! " and if you do
not, coils around iron will always be a Miss Terry.

------------------------------------------------------------------------------------------------------------------------------
(E) Testing chokes for CLC filters with Idc, setting the air gap.
I have sometimes had to supply filter chokes or SE OPTs to people building tube amps and have
set the air gap prior to the sale but without the real amp circuit present.

Fig 2.
Test schematic for measuring choke L with Idc, and setting air gap.

The Fig 2 circuit will allow safe measurement of a filter choke using a cheap 30VA PT
12.6Vac secondary for up to 2.4Aac. 2 x 1N5408 Si diodes are used with 2 x 470uF
caps in a doubler rectifier to make up to 34Vdc at 0.8Adc. Providing the Idc and C values
are the same as in an amplifier with a much higher B+, the 100Hz Vac ripple calculations
and filtering action of the CLC will be exactly the same. The Idc is 270mAdc for the anode
supply for 4 x EL34 plus driver stage.

(1) Any surplus transformer with winding over 12.6Vrms to 30Vrms may be used in either
bridge, full wave, or doubler config to give Vdc at C1 not higher than +40Vdc, but be aware
of the VA rating. The choke has Rw 26r, R1 is adjusted so Idc = 270mAdc in this case.

(2) The air gap must be adjusted to maximize the inductance to get high Vac attenuation
but not have the choke become saturated.
Fig 2 shows the Vr before and after L, and with L1 air gap adjusted for optimum.
100Hz attenuation factor = Vripple after choke / Vripple before choke = 4mVrms / 2.5Vrms
= 0.0016, or 1 / 625.
XC2 470uF = 3.38r at 100Hz. XLP = 625 x XC2 = 625 x 3.38r = 2,112r
Thus L = 2,112r / ( 6.28 x 100Hz ) = 3.36H.
The Rw of 26r has almost no influence on design, but the the Idc flow heats the wire and
heat power = Rw x Idc squared = 26 x 0.27A x 0.27A = 1.9W, and the temperature rise
may be calculated according to table for power / sq.ins. A choke less with slightly less surface
area than a tennis ball should withstand 1.9W.

(3) The choke may first be set up with Is tightly butted against Es, and even without any
air gap the butted join acts like there has been an air gap added.
So for a core rated for max µ between 10,000 to 2,500 with maximum intermeshing may have
hard butted µe = 2,000 to 700 approx, without any real air gap. Butting a pile of E against I pile
means the grain direction of Is and Es changes direction by 90 degrees, and this much reduces
µ by making the effective ML behave as though it is longer than it really is, and this is similar
to adding a small air gap, even though no real air gap exists.

Therefore placing a real air gap should follow the formulas for µe and air gap. Butted µ should be
considered to be say 1,000 in calculations.
Where µ = 1,000, it is high enough for many core with Idc to become saturated, ie, Bdc is between
1.0Tesla for low grade iron to 1.6Tfor good GOSS E+I.

(4) The 100Hz Vr at C1 = Idc x 2,200 / C in uF, Vrms. 2,200 is constant for 100Hz ripple.
For Vr 120Hz, use 1,833 instead of 2,200.
For Fig 2, Vr at C1 = 2.5Vrms.

If the core is saturated, the Vr at C2 will be higher than expected as the Iac flows from C1 to C2 via
the Rw 26r without much attenuation by inductance. The CLC becomes CRC, and Vr at C2 could
be 0.32Vrms.
Adding a small air gap with a sheet of paper ( say 0.07mm ) right across the space between E and I
may reduce Bdc to below saturation, and allow the choke to work as a pure inductance.
This total gap = 0.14mm, because there are 2 gaps around the magnetic length which is the centre
line in steel around each window.
The Vac at C2 should reduce, but if not much, add another sheet of paper for 0.14mm, and air gap
= 0.28mm, and you get less Vac at C2. You can keep adding sheets of paper until Vac at C2 is very
low and then if any more sheets of paper are added, the Vac at C2 begins to rise. This means the
air gap is too large, the choke L has begun to reduce because µe has become too small.
So use the number of sheets of paper that give Vac minimum at C2.

(5) The air gap is correct when the wanted Idc is flowing, and the Vr at C2 is at its minimum.

The measurement of Vac across C2 is almost impossible to do with a DMM or analog meter
because the +Vdc rail will contain a lot of noise below 30Hz because the mains level is constantly
changing due to the hundreds of other ppl sharing your 240V mains supply.
Its expensive to regulate the +Vdc rail, and the simple option is to use a RCRC filter with -3dB
pole at 50Hz, say 0.33uF + 10k0 and two cascaded filters give -3dB at 70Hz with only -1dB at 100Hz
but - 40dB at 7Hz and more below that and then the CRO trace used to see the Vac at C2
will not bounce up and down so much you cannot see what you want to measure. The CRO screen
should have a piece of tape alongside giving between 0 and 1mV with range setting for smallest
Vac range.

There is no way of knowing exactly what the Bdc may be for a choke with Idc because µe cannot
be exactly known, but it can be calculated if N, Vac, Afe and F is known.

Measuring L of choke without Idc is not best practice because the addition of Idc will reduce
slightly the µe without Idc and best measurement  is done with Idc flow equal to what is found
in the amp where choke is to be used.

The wave at C1 will be a sawtooth or triangular wave which contains many even numbered
H products, ie, 200Hz, 400Hz. The Vac at C2 will have mainly only 100Hz.

(6) The paper thickness must be known. A 128 page exercise book has 64 sheets and has
4.7mm total thickness not including cardboard
covers. Each paper sheet thickness = 4.7mm / 64 = 0.073mm. It is important to measure the gap.
Paper is OK for a permanent gap if well soaked with varnish before bolts and yokes are drawn up
tight. Re-measuring after tightening bolts should give the same results.
Soaking the choke in a can of varnish before bolts are tight is best way to wet all surfaces.
When bolts are tightened, excess varnish can flow back to can. The choke may be heated
slightly to dry and harden varnish.

(7) The 470uF or more between OPT B+ connection to 0V contains a huge reserve of energy,
like a battery, and transients in music in class AB amps pull the extra instant Iadc from this
capacitance, say C2. In all the cases of 30W AB amps, rarely does the B+ move more than +/- 1V
even with very loud music passages. If Idc falls below the rated Idc, Inductance slightly increases,
and filtering is improved. The choke value swings a little in response to the Idc demands.
---------------------------------------------------------------------------------------------------------------------

(F) Resonance in CLC filters.

Fig 3.

Fig 3 shows the same 470uF caps and 3.36H choke in CLC for a tube amp.

Wherever there is a CLC ripple filter as in Fig 3 above, there will be series resonant behavior
between L1 and C2.
The resonant F = Fo = 5,035 / sq.rt ( LmH x CuF ).
If the L = 3,360mH, and C2 = 470uF, then Fo = 4.0Hz. At 4.0Hz, XL = XC = 84r.

The 100Hz Vr at C1 is generated by diodes and HT winding on PT. I show R1 source
resistance for Mains, which may vary, but is usually < 5r0 for 240Vac Mains.
The PT has R2 Rw = about 2.5% of the primary load. R3 secondary Rw may be 2.5%
of the sec load estimated at 200r. The Si diodes have R < 1r0, so may be ignored.
But total source resistance of Vdc supply including C1 may total about 5% x Vdc / Idc = 5%
of 1,555r = 78r. It is much higher if there are tube diodes and HT winding Rw is deliberately
high to make sure the Rw limits the peak charging current in tube diodes to their rating
which is many times less than max peak Iac in Si diodes.

The F response graph is typical for CLC filter in a B+ PSU. For the flattest F response for
L1+C2 below say 10Hz. R6 should be = 1.414 x XL
at 4Hz = 118r.

But R6 shown is the load of the tubes shown here = 1,514r, and this is not low enough to
reduce Q of L1 and C2.
To damp the resonance, R could be in series with L1 and C2, so R5 could be added to
ensure the flat response.

Flattening the F response means that the noise between 2Hz and 8Hz created by
mains Vac level changes can be reduced by -10dB.

The L1 Rw of 26r does some damping, but 26r is too low to do all damping, so R5 may be
118r - 26r = 92r, where Vac source resistance
= 0.0r. When I plotted the response above, the test circuit may have had very low source R.
If source R = 78r, then peaking
will be low, maybe less than +2dB, and R5 omitted. In theory, R5 = 118r - 78r - 26r = 14r,
so may be omitted.
If the choke is allowed to have high Rw, it just gets too hot.

It is surely easy to build an amp where CLC has a peaked LF response with Fo resonance
between 3Hz and 15Hz where the 10Hz at C2 connection at OPT is higher than at C1.
If C2 = 3 parallel 470uF = 1,410uF, Fo = 2.3Hz, and the XC2 = 49r. The R for non peaked
response = 68r, and if Rw = 26r, and
source R = 78r, there should be no peak in LF response. But this does not means there
will be no LF below 15Hz at C2. There is always some.

Typical LF at C2 below 15Hz = 0.03Vac, and well above the 100Hz level of 0.004Vac.
Noise with F below 10Hz usually cannot easily reach the listening ear because speakers
cannot reproduce it, and we cannot hear it, and if the amp is a PP type, the OPT common
mode rejection action prevents such LF noise getting to OPT Sec.The effect on amp operation
of B+ wobbling up and down +/- 50mVpk is entirely negligible. The mains should be able to
be switched on and off at 1 second intervals and no change in sound should occur.
I have never seen a need for B+ regulation, not even with SE amps which have no benefit
of common mode rejection of rail noise
with a PP OPT with CT.
--------------------------------------------------------------------------------------------------------------------------------
(G) The alternative to CLC is CRCRC with more C and maybe more R.
For worthwhile 100Hz attenuation factor = 0.1, a section of R+C should have R > 10 x XC.
If the B+ = +420Vdc at C1 235uF, and we allow B+ reduction of 5% with filter,
the Vdc output after filter = +420Vdc - 5% = +399Vdc. The Vdc across filter R =
( 420Vdc - 399Vdc ) / 0.27A = 77r, and it must have 15W rating.

If CRCRC is used, each R = 38.5r, say 3 x 100r x 5W ea in parallel for R = 33r.
If C = 470u, 100Hz Xc = 3.4r so attenuation = 0.1 approx, so at C3, expect Vripple =
2.5Vrms x 0.1 x 0.1 = 0.025Vrms.
If C2 and C3 = 940uF each then Vripple at C3 = 2.5Vrms x 0.05 x 0.05 = 0.0063Vrms
which I suggest is quite low enough for any amp, and there will be no problem with
LF resonance.

I could argue that the choke is good, but the extra 3 x 470uF plus 6 x 100r are going
to be cheaper, and not use up too much space on chassis. There will be no resonant LF
behavior for the CRCRC.

One problem with a total of 6 x 470uF in B+ supply is the inrush Ia needed to charge
them all up after amp turns on. Series Rw at PT primary may be 40r, so where heater
filaments are cold, and 6 x 470uF have no Vdc, peak input current could be high enough
for long enough time to blow a 4A slow-blow fuse which can withstand 4A average with
higher peaks.

My common solution to reducing high inrush Iac to at least 1/2 the value was to have
about 80r in series with primary of PT, and then have a relay which shunts the 80r after
about 4 seconds. So B+ reaches about +280Vdc in about 3 seconds with a 2A slow fuse,
and when 80r is shunted, B+ continues to +420Vdc, and the second surge of high input
Iac is no more than the first, so the 2A fuse does not blow. Normal mains power input for
say 4 x KT88 in 5050 may be 200W, so Iac = 0.83Aac, so the fuse should blow when
something causes Iac input to increase to say 2.4A. The 4A fuse may allow something
to heat up and catch fire before a fuse blows.
A delayed B+ on every tube amp is not a bad idea, even where CLC with less C is used.
The delay should work where amp is switched off, then on again within 2 seconds.
The LC filter is a simple good filtering solution but the LF resonance should be kept
below 5Hz. The amp should have C+R input network to attenuate input below 5Hz.

With a preamp, the Idc is much less, and tube load is usually much higher ohms than
in a power amp so a choke is never needed. Plain CRCRC filters work very well without
wasting much power in hot resistors. A shunt regulator at preamp input stages usually
keeps the VLF from appearing at output, especially where there is a MC phono amp
which has very high LF gain, and where there is a possibility of LF oscillations.

(H) Any choke in a CLC supply may be bypassed with suitable R+C in series to
make a damped parallel resonant L+C 100Hz.

See Fig 3, R7 = 56r, more than Rw, and C3 = 0.8uF. C is polyester 630V rated, and
calculated when the choke inductance is known, then adjusted in circuit for least V2 at C2.
For L = 3.36H, C will be about 0.8uF. This will reduce 100Hz at C by -10dB, but some
200Hz and 400Hz manage to pass, but will remain below 2mVrms at C2.
-------------------------------------------------------------------------------------------------------------------
(I) One very good method to design a filter choke for CLC use is to work from
first principles with Hanna's method clearly spelled out in the Radiotron Designer's
Handbook, 4th Ed, 1955, pages 247 to 250. But I have never found time to convert
Hanna's Method to metric units which were introduced to Australia in the 1960s, so
anyone using Hanna's Method will have to work with inch dimensions.
There is another good little book, 'Coil Design and Construction Manual' B.B. Babani,
first printed 1960, except that it does not delve into air gap setting very well.
When I use Hanna or Babani to check my design for a choke, I must go back to using
Imperial measures of inches which I still know well, but its a Royal PIA for ppl who
never used inches and feet, and know only Metres, M, and millimetres, mm.

(J) Design a choke for 270mAdc, and with L up to 6H.
Not all of you will beg borrow or steal a copy of RDH4, and most men never read books
any more.
I offer an alternative and include a typical example most everyone will find useful at
some time if they build any tube amp supply which needs a supply from 50mAdc to
270mAdc, and for any B+ voltage from +250Vdc to +550Vdc. It is not to dissipate
more than 4W in Rw.

(1) Calculate wire size.
Current density for design should be 2Adc / sq.mm. This usually allows a fault condition
where Idc could double for a awhile without heat damage to wire and insulation.

For 2A / sq.mm, Cu section area = Idc / 2A / sq.mm.
So for 270mA, Cu area = 0.27A / 2 = 0.135sq.mm and Cu dia wire = sq.rt ( Cu area x 28 / 22 )
= sq.rt ( 0.135 x 28 / 22 ) = 0.414mm.
You could try 0.40mm Cu dia x 0.462mm oa dia, see wire table 1 :-

Table 1.
Wire sizes for Grade 2 winding wire.

Table 2. Choke details based on based on T25mm x S25mm wasteless E+I, with
area in bobbin for wire = 34.0mm x 10.0mm = 340sq.mm.
 Cu wire dia, mm turns, max. Resistance, ohms DC current max L, Henry µe =200 0.20 4,800 380 89mA 25.0 0.25 3,100 157 138mA 10.8 0.30 2,200 77 197mA 5.4 0.35 1,600 42 267mA 2.88 0.40 1,300 26 339mA 1.9 0.45 1,050 17 420mA 1.24 0.50 870 11 522mA 0.85 0.60 600 5.3 752mA 0.40 0.75 390 2.2 1.16A 0.17 1.00 230 0.73 2.02A 0.06 1.40 120 0.19 4.0A 0.016 2.00 60 0.05 7.7A 0.004
Note. Above I said 0.40mm Cu dia x 0.462mm oa dia could be used and window
winding area = 340sq.mm.
The table suggests turns = 1,300t for 0.4mmCu wire.
Neat layer winding and 0.05mm insulation will allow tpl = 0.97 x 34mm / 0.462mm = 71t.
The winding height of 10mm allows no of layers = 10.0 / ( 0.462mm + 0.05mm )
= 19.53 layers, but you should 20.0 layers so total turns = 71tpl x 20L = 1,420t.
Random winding will allow about 1,300t.

(2) Calculate Rw.
Rw = TL x N / ( 44,000 x Cu dia squared ).
For T25mm x S25mm, TL = 138mm. Rw = 138mm x 1,420 / ( 44,000 x 0.4mm x 0.4mm )
= 28r.
Heat in winding = Rw x Idc squared = 28r x 0.27A x 0.27A = 2.04W.

On page 238, RDH4, there is Fig 5.18B giving Temp rise versus W / square inch of
external core area.
Graph 1. Power transformer temperature rise, degrees C for Watts heat loss per sq.inch.

SA = T x [ ( 15 x T ) + ( 11 x S ) ].
For T25mm x S25mm wasteless E+I, T = S = 1 inch.
SA = 1 x [ ( 15 x 1 ) + (11 x 1 ) ] = 26 sq.ins.
Heat per sq.in = 2.04W / 26 = 0.078W / sq.in and T rise = less than 15C.
There is no heating of core from high Bac, so choke runs cool.

(3) What are other core T size options?
Try T32mm x S32mm for Afe = 1,024sq.mm. Winding area = 43mm x 12.8mm = 550sq.mm.
For 0.462 oa dia wire, expect get 90tpl x 25L = 2,250t, maybe 2,000t with random l winding.
TL = 180mm. Rw = 2,250 x 180mm / ( 44,000 x 0.4mm x 0.4mm ) = 58r.
For 270mAdc, Heat = 4.22W. SA = 40sq.in. W / sq.in = 4.22 / 40 = 0.1055W / sq.in.
Temp rise = 15C. running temp = 40C = OK.

(4) To avoid complete reliance on Table 2 above, Calculate µe for T25mm x S25mm.
Bdc = 12.6 x N x Idc x µe / ( 10,000 x ML ) where Bdc is Tesla, 12.6 and 10,000 are
constants for all such equations, Idc is Amps dc, µe is effective core permeability
with air gap, ML is iron magnetic path length around each window in mm.
For 1,420t, Bdc for GOSS core can be 1.0Tesla = 12.6 x 1,420t x 0.27A x µe / ( 10,000 x 138mm ).
Thus µe = 1.0T x 10,000 x 138mm / ( 12.6 x 1,420t x 0.27A ) = 286.

(5) Calculate L for µe = 286, T25mmx S25mm.
L = 1.26 x Nsquared x Afe x µe / ( 1,000 x ML ) where L is Henry, 1.26 is a constant,
N is thousands of turns, Afe is centre led area = Tmm x Smm, µe is effective permeability
with air gap, ML is iron magnetic path length around each window.
For this choke, L = 1.26 x 1.42th squared x 25mm x 25mm x 286 / ( 1,000 x 138mm ) = 3.3H.

(6) Calculate L for T25mm x S50mm.
For same 1,420t, µe, 0.27Adc, ML,
L = 1.26 x 1.42 squared x 25mm x 50mm x 286 / ( 1,000 x 138mm ) = 6.6H.

(7) Calculate ue for T32mm x S32mm and for N = 2,250t x 0.4mm Cu dia wire in (3),
ML = 180mm.
µe = 1.0T x 10,000 x 180mm / ( 12.6 x 2,250t x 0.27Adc ) = 235.

(8) Calculate L for T32mm x S32mm, µe = 235.
L = 1.26 x 2.25th squared x 32mm x 32mm x 235 / ( 1,000 x 180mm ) = 8.5H.

(9) Calculate Air gap size, Ag.
µ max for close butted GOSS E+I, no real air gap = 1,000, approximate.
Now it can be proved ( elsewhere ) that
µe = µ / [ 1 + ( µ x air gap in mm / ML of iron in mm ) ]

From this, Ag = ML x [ (1 / µe ) - ( 1 / µ ) ].
For T25mm core above, µ = 1,000, µe = 286,
Ag = 138mm x [ ( 1 / 286 ) - ( 1 / 1,000 ) ] = 0.34mm.

This the total gap, so the two gaps in ML each need gap material = 0.170mm.
Confirm Ag size when choke in use with 270mAdc.
The stack Smm does not make any difference to needed µe or Ag, but stack height will
determine L and Bac which depends on Afe.

(10) Calculate Ag for T32mm core,
For 32mm x 32mm core, µe = 235, µ = 1,000, ML = 180mm,
Ag = 180mm x ( 0.004255 - 0.001 ) = 0.585mm,
Use gap material = 0.293mm, but confirm AG size when choke in use with 270mAdc.

(11) Maximum Bdc should not exceed about 1.0Tesla for GOSS chokes for CLC.
Max total Bdc+Bac can be 1.5Tesla for GOSS choke, so Bac can be up to 0.5Tesla.
Ripple Vr frequency for full wave rectifier = 2 x mains F, 100Hz ( or 120Hz in USA. )
Bac = Vrms x 226,000 / ( Afe x N x F ), where 226,000 is a constant.
Max Vrms = Bac x Afe x N x F / 226,000.

The 100Hz Vac across choke is approx = Vac at C1 - Vac at C2 and where Vac at
C2 is less than 0.1 x Vac at C1, then Vac across L = Vac at C1.
For this example, Vac at C1 = 2.5Vrms.
Bac = 2.5V x 226,000 / ( 625sq.mm x 1,420t x 100Hz ) = 0.006Tesla.
This is a very small Bac, and Vac at C1 could theoretically be 198Vrms.

In most CLC rectifier filters, 100Hz Vac across the choke will be less than 25Vrms
where Bac = 0.06Tesla, a tiny value, with means the Bdc could be higher than
1.0Tesla.
Bdc could be 1.2T and ue would be 334 with smaller Ag. L would be 3.8H,
so the 100Hz attenuation factor increases, but only slightly. I prefer Bdc = 1.0Tesla
to allow for where Iadc increases in class AB amp and for short time operation
immediately after amp turn on.

(12) Tube rectifiers of any kind will arc internally and then fail to become
useless if reservoir C exceeds values stated in data sheets for the wanted Idc.
The data sheets also say what the series resistance should be between HT
winding and tube diode. In old days, the HT winding always had a CT taken to 0V,
so only 2 diodes are needed, and many rectifier tubes have 2 diodes with a common
cathode to suit the use, such as GZ34, one of the best I could ever use for +420Vdc,
and OK for 135mAdc with C1 = 33uF.
but for 270mAdc, I would use 2 x GZ34 and 66uF or slightly less.
The Idc can double for class AB2, and to avoid the excessive peak charge Idc,
the C1 can be kept at 33uF for the 2 x GZ34.
The Vac to Vdc conversion ratio with low reservoir C may be only 1.1 so for +420Vdc,
the HT winding is 420Vdc / 1.1 = 380Vrms - 0V - 380Vrms. Without any load the B+
= +537Vdc, so all caps in CLC should be 350V rated but in series pairs.
Thus the CLC filter could be C1 = 34uF 2 x 68uF in series,
L = 6.6H with T25mm x S50mm,
C2 = 235uF = 2  x 470uF in series.
100Hz Vac at C1 34uF = 0.27A x 2,200 / 34uF = 17.5Vrms. 100Hz attenuation factor
= XC2 / XL = 6.8r / 4,148r = 0.0016, so 100Hz at C2 = 0.028Vrms = OK.
Fo for 6.6H and 235uF = 4.0Hz = OK.

The RLdc = 420Vdc / 0.27A = 1,555r and time constant with C = 34uF = 0.053Sec.
The Vpk-pk for C1 100Hz saw tooth wave = 17.5Vrns x 3.3 = 58Vpk-pk.
Where Idc is constant, the +420Vdc at C1 would fall to 0V in 0.05S, so this is
( 420V / 0.053S ) V / S = 7,924V / S and to reduce 58V the time = 58V / 7,924V = 0.0073S
This occurs during the time for each 50Hz 1/2 wave = 0.01S, so the diode charges the
34uF for 0.73 of each 1/2 wave, so average charge current = 0.27Adc x 1 / 0.73 = 0.369A.
Average Ia for each diode of one GZ34 = 0.369A / 2 = 0.185A, and peak Ia = 0.185A / 0.63
= 0.293A.
GEC data for 5AR5 = GZ34 peak Ia for each diode = 0.82A pk, so I think what I propose
here is OK, but the GZ34 made now in China or Russia may not be equal to what was made
in 1960.
The Vdc regulation with GZ34 will give PSU B+ output resistance of about 200r.
So if Idc increases from say 270mAdc to 540mAdc, the Vdc drop = -54Vdc, so you could
never get the 90W per channel; you could only ever get instant Po of 90W.
In practice, when an amp is tested with pink noise that is bandwidth limited to 20Hz to
20kHz, the peaks in noise waves will be seen to begin to clip when average Po = 0.1
x maximum available instant Po, so 9W.
For hi-fi the GZ34 is OK until a tube loses its bias control and draws much more Idc than
normal. 1 x GZ32 used to be used for 2 x KT66 but 1 x GZ34 are needed for 2 x KT88,
and Quad-II-Forty used 1 x 5U4 which I sure did not like.

Choke input, ie LC filters with tube rectifiers works MUCH BETTER than CLC because
peak diode currents are much lower. The regulation is better.

(K) Winding chokes.
Neat layer winding methods are best where patience, skill, and machine lathes allow.
These days polyester-imide coated high temp grade 2 winding wire is much more rugged
than fragile enamels of the past and wire can be wound on using the "random winding"
method.

This means the wire is fed onto bobbin without layering neatly, and turns are allowed to
pile up while slowly traversing the wire across the bobbin width. This makes all the wire
crossings at a small angle so pressure between wires on wires is not great. Wire is wound
with minimum tension, and varnish can be painted on every 200 turns so at the finish of
winding all turns are soaked in varnish. Towards the top of the winding, hills and valleys
in the level of turns is minimised by feeding more turns into valleys than on hills, so you
end up with height of winding that is all within 2mm of maximum height.
Two pack epoxy slow set varnish is best.

After a final varnishing, wind two layers of flexible insulation tape over all wire. Thus
arcing cannot occur between iron core and coil wire. Terminations on the bobbin should
be provided where wire is less than 0.75mm dia.

People may find some old and useless transformer with an open winding which may yield
a suitable amount of iron for a choke. Chokes in PSU do not demand that the iron be top
grade GOSS. I often obtained E+I from re-cycled cores from fused transformers.
The bell ends and bolts are all removed, and then whole transformer is placed into a
small wood wood fire for 20 minutes and heat iron until just cherry red hot. The heat
vaporizes and burns off any plastics and varnish. Next day when the lams have cooled,
the E+I lams will all just fall out loose, and the heat will have annealed the iron and won't
affect the iron's magnetic properties.

Unfortunately many people won't be able to light a fire anywhere to fry old chokes and
transformers. But once the old iron is cooked the old wire can easily be sawn through and
removed to a re-cycling bin. Don't try cooling hot cores in water. Don't try to clean the
oxide layer off the laminations; it insulates the iron laminations from each other which
prevents eddy current losses. If the material is not 25mm tongue size, the turns and
current and wire size will have to be worked out to suit the window size.

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