Нашел по коакс. трансам.
Transmission Line Transformers
A transmission line conveys an electromagnetic signal from its input to its output. In other words, a transmission line can transport RF power from a generator to a load. The power is developed in the resistive portion of the load impedance, Zt = Rt + jXt. We typically call the characteristic or surge impedance of a transmission line Zo. An estimate of a particular transmission line's Zo can be found by measuring the input impedance to the line when it is terminated in a short circuit, and when it is terminated in an open circuit. Zo is then found to be the geometric mean of these two input impedances. Make your measurements at a frequency that creates input impedance values that are close to the highest accuracy range of your test equipment.characteristic impedance of line, Zo = sqrt ( Zsc Zoc)
Since the velocity of propagation of the electromagnetic energy along a transmission line is less than that of air, a wavelength in a transmission line is shorter than its free-space value. We normally assign 360 electrical degrees to a wavelength. Thus a physical quarter-wave section of transmission line with air insulation (velocity factor = 1.0) would be 90 degrees long. However the same physical length of line with solid polyethylene insulation would be about 136 degrees long, since its velocity factor is about 66 percent. We denote the phase shift across this line as negative 136 degrees to convey the fact that a time lag or delay is associated with the propagation of the energy from the input to the output. Note that the phase shift across a transmission line is dependent on Zt, and the value of -136 degrees in our example assumes that Zt = Zo. Also keep in mind that the voltage phase shift and the current phase shift are the same only when Zt = Zo.
Losses in a transmission line consist of dielectric heating (the dissipation factor of the insulation determines this), and conductor heating ( I2R ) caused by resistance to the RF current. The maximum rated power-handling capability of a transmission line is based on a fixed temperature increase, and assumes the line is terminated in its characteristic impedance (Zt = Zo). In general the larger the transmission line diameter, the lower the losses, and the higher the frequency, the higher the losses.
A transmission line electrically 90 degrees long can be used as a simple impedance transformer if we can select the Zo of this line, using the following simplified, lossless equation. Zo in this case would be the geometric mean of the load impedance and the input impedance. For example, if you wanted to transform a resistive load of 113 Ohms to 50 Ohms, Zo would have to be 75 Ohms. It may be helpful to think of this in terms of a -90 degree tee or pi network.
characteristic impedance of line transformer, Zo = sqrt (Zin Zt)
Note also that a 90 degree length of line looks like a parallel-resonant circuit at its input when it is terminated in a short circuit, and looks like a series-resonant circuit at its input when terminated in an open circuit. Just the opposite is true of a 180 degree length of line, where the termination impedance appears at the input to the line. That is, impedances repeat every half wavelength along a transmission line, if we ignore the effects of losses. The losses tend to pull the input impedance closer to Zo.
An interesting effect with a 45 degree (one-eighth wave) length of line is the fact that Zin is a reactance when Zt is a resistance other than Zo. And Zin is a resistance when Zt is a reactance. A 135 degree (three-eighth wave) length of line behaves similarly, except the sign of the reactance is reversed compared to that of a 45 degree length of line.
Here are the full set of transmission line equations for the lossy case:
Zin = [ Zt + Zo tanh ( y ) ] / [ 1 + (Zt/Zo) tanh ( y ) ] Ohms
dielectric constant, e = 1 / vel2
velocity factor relative to the speed of light, vel < 1.0
C = 1016 sqrt ( e ) / Zo pF / foot
L = 0.001016 Zo sqrt ( e ) uH / foot
Zo = characteristic impedance of line
note that Zo has a reactance term when loss is substantial, but the line is still terminated in Ro for a perfect match
y = a + jb
a = line loss (Nepers)
b = electrical length of line
tanh ( y ) = [ sinh ( 2a ) + jsin ( 2b ) ] / [ cosh ( 2a ) + cos ( 2b ) ]
1 Neper = 8.686 dB
- Подпись автора
73!
Александр, VE3KF, TO3T ex VA3QP, VE3XAX, VA3TTT.
Мой Ютуб канал: https://www.youtube.com/@Contester7/videos На продажу имеются 2 мои книги - по антеннам и по УМ.