# Wideband transformers II (types)

In the previous post I derived formulas that could be used to calculate inductors on ferrite and iron powder cores. In this chapter I present various types of transmission-line transformers. The goal in designing a good transmission-line transformer is to make it usable in matching generator with the load over a broad range of frequencies, therefore making it a wideband transformer.

From the functioning principle point of view there are two main categories of transformers:

– transformers based on induction in the core.

– transformers based on transmission line techniques that use the core only to isolate the output from input.

Induction transformer

One could employ a regular transformer design with primary winding and secondary winding on a ferrite core so that the impedance is matched between the generator and the load but it turns out that the more the number of turns is, the more parasitic capacities are and therefore the cutoff frequency for the transformer is lowered. A core with high permeability could be used to reduce the number of turns and therefore to reduce the parasitic capacities.

Since this type of transformer is based on the magnetic flux inside the core, any leakage in the flux will be seen as a loss. Coupling between primary winding and secondary winding is much more important and one could use different winding techniques in order to make the coupling better. For example primary and secondary winding could be put together when rolled on the core.

Magnetic Longwire Balun

This is a transformer made by RF-systems in 1988 and registered to that name (MLB). They claim to use a special ferrite to obtain a broad frequency range (0.1 to 40Mhz) in matching a longwire antenna. It is actually a 1:3 voltage UnUn.

Current induction transformer

This type of induction transformer is based on principle of two currents producing same value of induction in the core but with oposite directions so that inductions will cancel each other. This is exactly what happens inside a transmission line and therefore it is also known as a transmission-line transformer.

Transformers based on transmission lines

Model of a tranmission line

Inside a transmission line the electromagnetic fields of the two conductors cancels each other so that there is no radiating outside. Therefore it is not important for the differential electromagnetic field between the two conductors what is the form of the transmission line. However if we coil up the transmission line on a core we will make a much bigger impedance for the common-mode currents, allowing us to isolate the input from the output, thus allowing us to connect input to output in various ways. This method is used in designing transmission-line transformers and a model of transmission-line in which common-mode impedance $Z_{sleeve}$ is seen is presented below: Therefore if we have a decoupling between input and output then we have both conductors of the transmission line floating at the end,  we could feed a symetrical load like the following, making a BalUn: This design was called by Guanella (see below) Basic building block.

The 4x rule

We will see that for some designs the equivalent $Z_{sleeve}$ impedance will be connected in parallel with the generator. In order to minimize its influence on the generator impedance, we will use the rule saying that $Z_{sleeve-equivalent}$ will be four times the $Z_{in}$ impedance: $Z_{sleeve-equivalent}=4*Z_{in}$

Characteristic impedance

If we have a transmission line with $Z_{in}$ – generator imput and $Z_L$ impedance load, we could calculate a maximum power transfer between the generator and the load when characteristic impedance is: $Z_c=\sqrt{Z_{in} Z_L}$

Guanella and Ruthroff designs

These designs uses the following rules:

–  Currents in the coupled conductors of a transmission-line are equal in magnitude but opposite in phase (total coupling rule).

–  For every transmission-line the output voltage will be identical (magnitude and phase) to the input voltage (no loss rule).

– There is no other connection between the transformer input and output other than through the transmission-line (total decoupling rule).

In 1944 Guanella extended the previous design in an article called ‘Novel Matching Systems for High Frequencies‘ by adding two transmission-lines fed by the generator whose output are connected in series
to double the voltage(1:2 voltage, 1:4 impedance): In 1959 Ruthroff analysed the design of Guanella and came up with an article called ‘Some broadband transformers’ in which the output of the transmission line is added to the input to produce a double voltage (1:2 voltage, 1:4 impedance) Since the output is partially added to the input ( Bootstrap effect), this kind of design is more prone to errors when there is a unbalance in the load.

The various designs based on Guanella and Ruthroff will be discussed further on in this chapter.

Guanella 1:4 impedance

The following pictures presents the Guanella 1:4 UnUn and BalUn respectively together with relevant currents and voltages: $Z_{in}=\frac{u/2i}{2u/i}*Z_L=\frac{Z_L}{4}$ $Z_c=\frac{u/i}{2u/i}*Z_L=\frac{Z_L}{2}$

It can be seen that $Z_{sleeve}$ is at potential so that it become in parallel with the generator. $Z_{sleeve}=4*Z_{in}=Z_L$ – using the rule of 4x

It is interesting that the $Z_{sleeve}$ is given by the upper transmission-line since the lower transmission-line will have no differential voltage between its ends. The two windings could be done also on the same core.

Example: $Z_{in}=50 ohm$ and $Z_L=200 ohm$ $Z_c=100 ohm$ $Z_{sleeve} = 200 ohm$

Ruthroff 1:4 impedance

The following pictures presents the Ruthroff 1:4 UnUn and BalUn respectively together with the relevant currents and voltages: $Z_{in}=\frac{u/2i}{2u/i}*Z_L=\frac{Z_L}{4}$ $Z_c=\frac{u/i}{2u/i}*Z_L=\frac{Z_L}{2}$

It can be seen that $Z_{sleeve}$ is at potential so that it become in parallel with the generator. $Z_{sleeve}=4*Z_{in}=Z_L$ – using the rule of 4x

Example: $Z_{in}=50 ohm$ and $Z_L=200 ohm$ $Z_c=100 ohm$ $Z_{sleeve}=200 ohm$

Guanella 1:9 impedance

The following pictures presents the Guanella 1:9 UnUn together with relevant currents and voltages:  $Z_{in}=\frac{u/2i}{3u/i}*Z_L=\frac{Z_L}{9}$ $Z_c=\frac{u/i}{3u/i}*Z_L=\frac{Z_L}{3}$

It can be seen that Z across input is $2*Z_{sleeve}$ in parallel with $Z_{sleeve}$ giving $\frac{2Z_{sleeve}}{3}$ thus $\frac{2*Z_{sleeve}}{3}=4*Z_{in}=\frac{4}{9}Z_L$ – using the rule of 4x, thus: $Z_{sleeve}=6*Z_{in}=\frac{2}{3} Z_L$

Example: $Z_{in}=50 ohm$ and $Z_L=450 ohm$ $Z_c=150 ohm$ $Z_{sleeve}=300 ohm$

Ruthroff 1:9 impedance

The following pictures presents the Ruthroff 1:9 UnUn together with relevant currents and voltages:  $Z_{in}=\frac{u/3i}{3u/i}=\frac{Z_L}{9}$

For the $Z_c$ we observe that the two lines have different characteristic impedance: $Z_{c-upper}=\frac{u/i}{3u/i}*Z_L=\frac{Z_L}{3}$ $Z_{c-lower}=\frac{u/2i}{3u/i}*Z_L=\frac{Z_L}{6}$

For optimum transfer we need transmission lines with different characteristic impedance. $Z_{sleeve}=4*Z_{in}$

What we could see from the picture is that the outer conductor of the two transmission-lines are connected together, therefore they could be put on the same core.

Example: $Z_{in}=50 ohm$ and $Z_L=450 ohm$ $Z_{c-upper}=150 ohm$ $Z_{c-lower}=75 ohm$ $Z_{sleeve}=200 ohm$

Models using winding impedance:

When constructing Guanella transmission-line transformers using coils, the following is the equivalence with the transmission-line version (only BalUn is presented):  When Ruthroff transmission-line transformers are built using coils, the following is the equivalence with the transmission-line version (only BalUn is prezented):

Modeling characteristic impedance:

When making transmission-line transformers and not using transmission lines but cables either twisted or not, it is hard to make characteristic impedance resulted from the above formulas. One way to know the characteristic impedance is to calculate it with the following formula which gives the impedance of a bifilar cable: $Z_c=\frac{276}{\sqrt{\epsilon}}lg\frac{2D}{d}=\frac{120}{\sqrt{\epsilon}}ln\frac{2D}{d}$ where

D – distance between center of the cables

d – diameter of the cable $\epsilon$ – permeability of the cable dielectric (we’ll discuss it in the next chapter).

If D become larger then the characteristic impedance will raise. Therefore one can improve impedance matching by using isolator tubes around winding cables.

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