I am asked about my use of the term
Distortionless Lines from time to time, often in the vein of
they don’t exist, so why discuss them?
The concept derives from the work of Heaviside and others in seeking a solution to distortion in long telegraph lines.
The problem was that digital telegraph pulses were distorted due to different attenuation and propagation time for different components of the square waves.
Heaviside proposed that transmission lines could be modelled as distributed resistance (R), inductance (L), conductance (G) and capacitance (C) elements.
In each incremental length Δx, there is incremental R, L, G and C. Continue reading Do Distortionless Lines exist?
Several correspondents refer to my article Feasibility study – loop in ground for rx only on low HF – small broadband RF transformer using medium µ ferrite core for receiving use – 50:200Ω and suggest “I got it wrong, #73 is the proven material choice for such a thing, and a 2t primary is optimal”.
In fact, I did explore #73 as an option, this article presents some key comparisons. The two key statistics shown in this article provided the basis for selecting the design.
Note that the scales are different from plot to plot.
Where the magnetising impedance appears in shunt with an ideal transformer with Zin=50+j0Ω, Insertion VSWR can be calculated.
2t on BN73-202
5t on BN43-202
Continue reading Comparison of BN43-202 / 5t with BN73-202 / 2t for rx only on low HF – small broadband RF transformer – 50:200Ω
The article On the concept of that P=Pfwd-Prev discussed the question of the validity of the concept of that P=Pfwd-Prev, exploring an example of a common nominally 50Ω coaxial cable at 100kHz. The relatively low frequency was used to accentuate the departure from ideal.
This article digs a little further with analyses at both 100kHz and 10MHz.
A plot was given of the components and sum of terms of the expression for power at a point along the line.
Lets look at the power calculated from voltages and currents for the example at 100kHz where Zo=50.71-j8.35Ω and Zload=5+j50Ω.
Above, the four component terms are plotted along with the sum of the terms. Continue reading Transmission lines: departure from ideal Zo
Ferrite cored inductors and transformers saturate at relatively low magnetising force.
#61 material example
Lets work through an example of a FT50-61 core with 10t primary at 3.5MHz.
Magnetic saturation is one limit on power handling capacity of such a transformer, and likely the most significant one for very low loss cores (#61 material losses are very low at 3.5MHz).
Let’s calculate the expected magnetising impedance @ 3.5MHz.
Zm=0.966+j144Ω, |Zm|=144Ω. Continue reading RF transformer design with ferrite cores – saturation calcs
A review of transformer design
In a process of designing a transformer, we often start with an approximate low frequency equivalent circuit. “Low frequency” is a relative term, it means at frequencies where each winding current phase is uniform, and the effects of distributed capacitance are insignificant.
Above is a commonly used low frequency equivalent of a transformer. Z1 and Z2 represent leakage impedances (ie the effect of magnetic flux leakage) and winding conductor loss. Zm is the magnetising impedance and represents the self inductance of the primary winding and core losses (hysteresis and eddy current losses). Continue reading RF transformer design with ferrite cores – initial steps
An online expert recently advised:
…The spec for type 43 makes it clear that it should never be used for HF unun construction. It is specifically engineered with a complex permeability that makes the core lossy on most HF frequencies. Since an unun is not a TLT (transmission line transformer) but rather an autotransformer, a low loss core is essential for efficient operation….
Now it contains the very common FUD (fear, uncertainty and doubt) that masquerades as science in ham radio, but without being specific enough to prove it categorically wrong. To a certain extent, the discussion goes to the meaning of
efficient operation. Continue reading An online expert on the unsuitability of #43 for HF UNUNs
On the concept of that P=Pfwd-Prev discussed the expression for power at a point on a line in terms of the travelling wave voltage and current components.
The expansion of P=real((Vf+Vr)*conjugate(If+Ir)) gives rise to four terms.
This article looks at the components of that expansion for a mismatched line for a range of scenarios.
- Lossless Line;
- Distortionless Line; and
- practical line.
We will override the imaginary part of Zo and the real part of γ (the complex propagation coefficient) to create those scenarios. The practical line is nominally 50Ω and has a load of 10+j0Ω, and models are at 100kHz.
A Lossless Line is a special case of a Distortionless Line, we will deal with it first.
A Lossless Line has imaginary part of Zo equal to zero and the real part of γ equal to zero.
Above is a plot of the four components of power and their sum at distances along the line (+ve towards the load). Continue reading From lossless transmission line to practical – Zo and γ
A reader of On the concept of that P=Pfwd-Prev asked if / how the scenario discussed could be modeled in SimSmith.
SimSmith uses different transmission line modelling to what was used in that article, but a SimSmith model of RG58A/U allows illustration of the principles and it will deliver similar results.
Let’s explore the voltage maximum and minimum nearest the load to show that VSWR calculated from the magnitude of reflection coefficient is pretty meaningless in this scenario.
Above is the basic model. I have created two line sections, one from the load to the first voltage maximum, and another to the first voltage minimum where I have placed the source. I have set Zo to the actual Zo of the line as calculated by SimSmith (56.952373-j8.8572664Ω), effZ as SimSmith calls it, so the Smith chart relates to the real transmission line. Continue reading SimSmith example of VSWR assessment
Some recent articles discussed some effects that in part are a result of Zo having a complex value (ie a non-zero imaginary part). Continue reading On working with complex Zo
The article On negative VSWR – Return Loss implications raised the question of the validity of the concept of that P=Pfwd-Prev.
The Superposition Theorem is an important tool in linear circuit analysis, and is used to find the combined response of independent sources. Superposition applies to voltages and currents, but not power. Continue reading On the concept of that P=Pfwd-Prev