----- Original Message -----
From: "Andy" <[email protected]>
To: <[email protected]>
Sent: Tuesday, March 29, 2005 4:06 PM
Subject: LF: Re: More on cores...
For a sinusoidal waveform, the minimum number of turns on a core is given by
:
V(rms) = 4.44. F . N . A . B where
V is the voltage across the winding
F is the frequency in Hz
A is the core cross sectional area in m^2
B is the peak flux in Teslas
To avoid excessive dissipation, for modern ferrites if you keep B to a value
of 0.2T or less you will be OK.
As an example, for a core of 15mm diameter (approximately an ETD49 core)
used in a 700 Watt PA the 50 ohms winding is calculated as follows :
V = SQRT(700 * 50) = 187V(rms)
This corresponds to a cross sectional area of 177mm^2, or A = 177*10^-6
m^2
V = 187, F = 137000, B = 0.2, A = 177E-6
N(min) = 187 / (4.44 * 137000 * 177E-6 * 0.2) = 8.7 Turns
Taking to the nearest integer above, you will at least need 9 turns for this
winding. You could use more turns to get B even lower, but now the copper
losses begin to increase as the wire length rises so adding a couple of
turns to get B even lower is the most you really need to do, so 10 to 11
turns is about right for this core.
Note that the type of ferrite is not important, all transformer ferrites
saturate as you get near 0.3T, althoug h modern ones MAY allow a bit higher.
This equation seems to suggest that any size of core is acceptable for any
voltage provided enough turns are used, and in a way this is true, but
getting higher power through the core needs larger cross-sectional area.
The calculations here are more involved, and it is easiest to resort to the
data sheets and look at what the manufacturer claims is the maximum rating
for any particular core.
As a guide line, on my switchmode PA that generated RF direct from 340 Volt
rectified mains (see QEX November/Dec 2002) I found an ETD49 sized core
using 3C85 material would happily carry 700 Watts with B kept to below
0.18T. The primary winding operating at 29 ohms load impedance was made
with 3mm diameter plastic covered Litz wire, and the secondary winding for
matching into 50 to 150 ohms antenna resistance from 1mm diameter enamelled
wire. At 700 W continuous operation for several hours in UK summer
temperatures, the transformer core sat around 60 - 70 degrees - comfortably
within its rating
Andy G4JNT
Hello Andy
I must admit that I am not too happy with your suggestion for
0.2 to 0.3 T. Ferrite manufacturers may in their catalogues mention
such values of B, these values are, however, for low frequencies,
typically 10 kHz.
As for the loss components in ferrites, eddy current loses are mainly
frequency dependent and hysteresis losses are mainly dependent on
magnetization.
In my suggestion to Dick, I used a figure for B of 40 mT. This figure comes
from a formula I have been using for many years. My formula is fairly
conservative with regard to core losses and it also ensures that the
intermodulation caused by the nonlinearity of the magnetizing current
is negligible.
My formular for a recommended safe B is:
B equal to 15 divided by the square root of the frequency, B being in
milliTesla and F in MHz..
This formula is in acordance with recommendations of e.g. the
ferromagnetic material producer AMIDON and, I think,
also with the pratice of designers of solid state wideband power
amplifiers.
73
Niels, OZ8NJ+
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