# A simple transformer model of the Guanella 1:4 balun – some further observations

A simple transformer model of the Guanella 1:4 balun discussed a simple model for the operation of the device, but a model that is too simple for most RF baluns. Notwithstanding that, it does expose some interesting issues that are not only valid at lower frequencies, but will also be manifest in an RF balun.

Consider the effect of breaking the connection at the red X, so that we now have  what is often referred to as an “isolated load”.

### Rules

An ideal 1:1 transformer obeys the following rules:

• Rule1: magnetising current is approximately zero;
• Rule2: the voltage across each winding is equal to the other;
• Rule3: the current through each winding is equal to the other;
• Rule4: the phase and magnitude of current in a winding is uniform; and
• Rule5: zero loss (ie no core loss, no conductor loss).

We can now add another rule to those:

• Rule6: if the load is isolated, and the transformers are identical, then the voltage across L1 will equal that across L2 (both +ve down), and both 0.5V1.

### Circuit analysis

1. Since the voltage across L1 is 0.5V1, the voltage across L2 is also 0.5V1 +ve down (by virtue of Rule2) and so the voltage at the top end of R1 is V1+0.5V1=1.5V1.
2. Since the voltage across L3 is V1/2, the voltage across L4 is also 0.5V1 +ve down (by virtue of Rule2) and so the voltage at the lower end of R2 is 0-0.5V1=-0.5V1.

So, the terminal voltages are not balanced, but the currents are balanced (so it is still working properly as a current balun).

Note that a two terminal impedance is a naive representation of many if not most antennas, popular, but a naive over simplification that does not facilitate evaluation of current balance.

## Single core balun

A popular practice is to wind all four windings on a single core. This essentially makes the voltage magnitude across L1 equal to that across L3, and in phase or out of phase depending on the winding orientation.

(Sevick 2001) proposed such a configuration, but noted that it only worked well on an “Isolated Load”. An isolated load does not need a balun, the currents must be balanced. This proposition is patent nonsense.

## Excessive magnetising current

In a practical balun, the current in L1,L3 comprises a component needed to magnetise the core and a component due to load current in L2,L3. If the load current is not much much larger than the magnetising current, the ability of the balun to ‘force’ current balance is compromised. Failure to achieve good current balance would mean that the terminal voltages will not be as they would if currents were balanced.

Excessive magnetising current is equivalent to low common mode impedance, a parameter often specified for a current baluns.

Note that common mode impedance of a Guanella 1:4 balun is approximately half that of the component baluns (Why the preference for Guanella 1:1 current baluns for HF wire antennas).

## An online example

Above is a model posted online to support an assertion about the failure of a Guanella 1:4 balun to perform in a given practical role.

Key issues include:

• The use of the transformer model for RF is probably too simple for reliable inference.
• It uses an isolated 200+j0Ω load which should beg the question about whether it is a good representation of the load otherwise described as a loop antenna.
• Using a truly isolated load, the currents at the load terminals are balanced, and the voltages will be determined by the division enforced solely by L2 in series with L3 ($$V_A=150 \text{ V, } V_B=-50 \text{ V}$$).
• Magnetising current through L2+L3, $$I_m=\frac{V_1}{2 \pi f (L_2 + L_3)}=0.159 \text{ A}$$ and the load current $$I_l=\frac{2 V_1}{200}=1 \text{ A}$$, relatively high Im for a good current balun (equivalent common mode impedance Zcm=0+j314Ω, which is very low for an antenna balun.)

Each of these issues are reason to dismiss conclusions drawn from the model as unreliable.

## References

• Sevick, J. 2001. Transmission line transformers 4th Ed. Noble Publishing Co. 9-15.