·The relationship between output power and magnetic core size

To increase the output power of the transformer, we hope to minimize the number of turns and make the wires as thick as possible under a constant voltage
This is beneficial for providing a larger current and outputting greater power. The former requires a larger cross-sectional area of the magnetic core, while the latter requires a larger window area of the magnetic core. Therefore, in order to obtain a larger output power, the magnetic core size must be large enough
The number of turns of the primary winding of a transformer can be calculated using the following formula:
N=k * 10 ^ 5 * U/(f * Ae * Bmax)
K is the ratio of maximum conduction time to period, usually taken as k=0.4;
U is the input voltage of the primary winding (V), (approximately equal to the DC input voltage);
F is the operating frequency of the transformer (KHZ);
Ae is the cross-sectional area of the magnetic core (cm2);
Bmax is the maximum allowable change in magnetic flux density (G)
Therefore, under a certain voltage, increasing the cross-sectional area Ae, increasing the operating frequency f, and selecting a larger peak magnetic flux density Bmax are all beneficial for reducing
The number of turns increases the output power. However, the core loss (iron loss) increases exponentially with Bmax to the power of 2.7 and f to the power of 1.7
Due to the limitation of magnetic core saturation, increasing the operating frequency f and selecting a larger peak magnetic flux density Bmax are both limited. Most are suitable for opening
The frequency of the ferrite core with power off is usually limited to 10-50KHZ, and Bmax is limited to 2000G (Gaussian). Generally, Bmax=1600G is taken
For suitability, the power is mainly controlled by the cross-sectional area Ae of the magnetic core, followed by the operating frequency f
But it must be clear that this control relationship is indirect rather than direct. Increasing Ae and increasing f only indicate that for the same voltage, allowing
The number of turns is less, and only by actually reducing the number of turns can the power be increased. If using the same material on a large magnetic core and a small magnetic core
Winding the same wire for the same number of turns results in essentially the same output power for the same input voltage. Similarly, if a well made transformer only
Simply changing the operating frequency will not increase the output power
Thinking of the problem with the landlord Zhang Weiming, as the transformer has already been installed, I suggest increasing the input voltage to increase the power; If from the transformer
If you want to purchase the device, you can try to thicken the wire appropriately and increase the frequency to allow for a decrease in the number of turns, which can increase the output
Output power
The wire thickening is limited by the window area Ac of the magnetic core. Using a wire with a cross-sectional area of Ad to wrap N circles, the occupied window area is:
Awc=N * Ad=k * 10 ^ 5 * U * Ad/(f * Ae * Bmax)
Assuming that the window occupancy coefficient of the primary winding is Sn=Awc/Ac, Ad is represented by the current I (effective value) and the allowed current density J, as
Ad=I/J/100, (Ad square centimeters, I-A effective value, J-A/square millimeters)
The above equation can be written as: Ac * Sn=k * U * I * 10 ^ 3/(f * Ae * Bmax * J)
Alternatively, U * I=Sn * Bmax * J * f * Ae * Ac * 10 ^ -3/k
Because the input power is equal to the product of the input voltage U and the average current value k * Ip, and the relationship between the effective current value I and the peak value Ip is
Ip=1.58 * I, so the input power Pi=1.58 * k * U * I=1.58 * Sn * Bmax * J * f * Ae * Ac * 10 ^ -3
Multiplying the efficiency Ef again yields the expression for the maximum output power
Po=1.58 * Ef * Sn * Bmax * J * f * Ae * Ac * 10 ^ -3
It can be seen that in addition to being directly proportional to the factors mentioned above that are beneficial for reducing the number of turns, the power is also proportional to the allowed wire thickness of Ac, Sn, and current
The density J is proportional. In engineering, it is generally taken as Ef=0.8, Sn=0.4, Bmax=1600G, J=4A/square millimeter, taking into account the different circuit forms
The winding structure is different, so the following equation is commonly used to estimate the maximum output power of the magnetic core: Po=m * f * Ae * Ac
Push pull circuit m=3.2, single ended forward circuit m=1.6, half bridge and full bridge m=4.48
The three commonly used U-shaped magnetic cores for TV line output transformers, U12, U16, and U18, have Ae and Ac products of 6.12, 14.9, and 30.4 (square centimeters), respectively. If the frequency is f=20KHZ and a push-pull circuit is used, the maximum output power that these three magnetic cores can provide can be calculated as:
U12: Po=3.2 * 20 * 6.12=548 W
U16: Po=3.2 * 20 * 14.9=954W
U18: Po=3.2 * 20 * 30.4=1945 W
This U-shaped magnetic core has a large window area and is suitable for high voltage and high power applications, but the magnetic circuit is long, the primary and secondary coupling is poor, and the leakage inductance is large. It is emphasized again that the calculated maximum power only indicates the ability of the magnetic core, which can be used in small quantities but not in small materials
After selecting the magnetic core, the maximum output power is related to the operating frequency
The following equation can be used for engineering estimation:
Po=1.6 * f * Ae * Ac (W)
F - Operating frequency (KHZ)
Ae - cross-sectional area of magnetic core (square centimeters)
Ac - window area of magnetic core (square centimeters)
(For other circuit forms, the coefficient 1.6 in the equation is different)
For EI40, Ae=1.28, Ac=1.5, it can be calculated that
When f=20KHz, Po=61W
When f=24KHz, Po=74W
When f=48KHz, Po=148W
The number of turns per volt of the winding is calculated using the following formula:
No=15.6/(f * Ae) (turns/V)
If f=24KHZ, No=15.6/(24 * 1.28)=0.51 turns/V
If the primary voltage V1=240V and the secondary voltage V2=36V, then
Primary turns: N1=No * V1=122 turns
Secondary turns: N2=No * V2=18 turns