Impedance (ohm) = 2 * 3. 14 159 * F (working frequency) * inductance (mH), and the setting needs 360 ohm impedance, so:
Inductance (mH) = impedance (ohm) ÷ (2*3. 14 159) ÷ F (working frequency) = 360 ÷ (2 * 3.14159).
Accordingly, the number of windings can be calculated:
Number of coils = [inductance * {( 18* coil diameter (inches)) +(40 * coil length (inches)}] coil diameter (inches)
Laps = [8.116 * {(18 * 2.047)+(40 * 3.74)}] ÷ 2.047 =19 laps.
The calculation formula of air-core inductance: L (MH) = (0.08 d.d.n.n)/(3D+9 w+10h).
D- coil diameter
Number of turns of n- coil
D-line diameter
H coil height
W-coil width
The units are mm and mH respectively. .
Calculation formula of inductance of air-core coil:
l=(0.0 1*D*N*N)/(L/D+0.44)
Coil inductance l unit: microhenre
Coil diameter d unit: cm
Coil turns n unit: turns
Coil length l unit: cm
Calculation formula of frequency inductance and capacitance:
l=25330.3/[(f0*f0)*c]
Operating frequency: f0 unit: MHz F0 =125khz = 0.125.
Resonant capacitance: c Unit: PF c=500... 1000pf can be determined by yourself or q.
Value decision
Resonant inductance: l unit: microhenre
1。 For a circular magnetic core, the following formula can be used: (iron)
L = N2。 Al l = inductance (h)
H-DC=0.4πNI/l N= number of turns of the coil (number of turns)
AL= inductance
H-DC= DC magnetizing force I= passing current (a)
L= length of magnetic circuit (cm)
For the vALues of l and al, please refer to the MIL comparison table. For example, when T50-52 material is wound for five and a half times, its L value is T50-52 (indicating that the outer diameter is 0.5 inch), and its al value is about 33nH after looking up the table.
L=33。 (5.5)2=998.25nH≈ 1μH
When the current of 10A flows, its L value can be changed from l=3.74 (look-up table).
H-DC = 0.4 π Ni/L = 0.4× 3.14× 5.5×10/3.74 =18.47 (after looking up the table).
You can know the degree of l value decline (μi%).
2。 Introduce empirical formula
L=(k*μ0*μs*N2*S)/l
In ...
μ0 is the permeability of vacuum =4π* 10(-7). (/kloc-negative seventh power of 0/0)
μs is the relative permeability of the iron core inside the coil, and μs= 1 when the coil is hollow.
N2 is the square of the number of coils.
Cross-sectional area of S coil, in square meters.
L the length of the coil, in meters
The k coefficient depends on the ratio of the radius (r) to the length (l) of the coil.
The unit for calculating inductance is Henry.
K value table
2R/l k
0. 1 0.96
0.2 0.92
0.3 0.88
0.4 0.85
0.6 0.79
0.8 0.74
1.0 0.69
1.5 0.6
2.0 0.52
3.0 0.43
4.0 0.37
5.0 0.32
10 0.2
20 0. 12
Inductance units and English symbols;
Since inductance was discovered by Henry, a foreign scientist, the unit of inductance is Henry.
Inductance symbol: l
Inductance units: Heng (h), Milli Heng (mH) and Micro Heng (uH). Their conversion relationship is1h =1000 MH =1000 000 uh. Remember, everyone
Transformer and inductance are closely related. Here we also introduce other expressions of units related to inductance:
R = average winding radius in inches.
L = physical length of winding, in inches.
N = number of turns
R = average winding radius in meters
N = number of turns
D = winding depth in meters (i.e. outside diameter minus inside diameter)
Main characteristic parameters of inductance
1 inductance l and its accuracy
Inductance l represents the inherent characteristics of the coil itself, which has nothing to do with the current. Except for special inductance coil (color-coded inductance), inductance is generally not marked on the coil, but with a specific name. The inductance of the coil mainly depends on the diameter, the number of turns and the presence or absence of iron core. Inductive coils require different inductances for different purposes. For example, in a high-frequency circuit, the inductance of the coil is generally 0. 1uh- 100ho.
The accuracy of the inductance, that is, the error between the actual inductance and the required inductance, depends on the application. The requirement for the oscillating coil is high, which is 0.2-0.5%. The requirements for coupling coils and high-frequency chokes are low, and 10- 15% is allowed. For some occasions that require high inductance accuracy, it can only be tested by instruments after winding, and O can be realized by adjusting the turn-to-turn distance near the edge or the position of the magnetic core in the coil.
2 inductance XL
The resistance of inductance coil to alternating current is called inductance XL, and the unit is ohm. Its relationship with inductance l and AC frequency f is XL=2πfL.
3 quality factor q
Coil quality factor
The quality factor Q is used to indicate the size of the coil loss, and the high-frequency coil is usually 50-300. The q value of the tuning loop coil is higher, and the resonant circuit composed of high q coil and capacitor has better resonant characteristics. The resonant characteristics of a resonant circuit composed of a low Q coil and a capacitor are not obvious. For coupling coils, the requirements can be lower, but for high-frequency chokes and low-frequency chokes, there is no requirement. Q value affects the selectivity, efficiency, filtering characteristics and frequency stability of the loop. Generally, it is hoped that the Q value will be larger, but it is not easy to improve the Q value of the coil, so it is necessary to put forward appropriate requirements for the Q value of the coil according to the actual use.
The quality factor of the coil is:
Q=ωL/R, where:
ω-working angular frequency;
Inductance of l- coil;
The total loss resistance of r- coil consists of DC resistance, high frequency resistance (caused by skin effect and proximity effect) and dielectric loss. "
In order to improve the quality factor q of the coil, silver-plated copper wire can be used to reduce the high-frequency resistance; Multi-stranded insulated wires are used instead of single-stranded wires with the same length surface to reduce skin effect; High-frequency porcelain with low dielectric loss is used as the skeleton to reduce dielectric loss. Although the use of the magnetic core increases the loss of the magnetic core, it can greatly reduce the number of turns of the coil, thus reducing the DC resistance of the conductor and improving the Q value of the coil.
The quality factor Q is a physical quantity representing the quality of the coil, and Q is the ratio of inductance XL to its equivalent resistance, that is, Q = XL/R. The higher the Q value of the coil, the smaller the loop loss. The q value of the coil is related to the DC resistance of the conductor, the dielectric loss of the skeleton, the loss caused by the shield or iron core, the influence of high frequency skin effect and other factors. The q value of the coil is usually tens to hundreds. Using magnetic core coil and multi-strand thick coil can improve the Q value of the coil.
4 Distributed capacitance
The capacitance between coil turns, between coil and shield, and between coil and bottom plate is called distributed capacitance. The existence of distributed capacitance reduces the Q value of the coil and deteriorates its stability, so the smaller the distributed capacitance of the coil, the better. The distributed capacitance can be reduced by using the sectional winding method.
5 Intrinsic capacitance
There are distributed capacitances between turns of coil windings, and there are also distributed capacitances between layers of multi-layer windings. These distributed capacitors can be equivalent to the capacitor Co connected in parallel with the coil.
6 Allowable error: the percentage obtained by dividing the difference between the actual value and the nominal value of the inductance.
7 Nominal current: refers to the allowable current of the coil, which is usually represented by letters A, B, C, D and E respectively. The nominal current values are 50mA, 150mA, 300mA, 700mA and 1600mA.