Real 4:1 Transmission Line Balun with Balanced Load
The circuit below shows a 4:1 transmission line current balun in operation feeding a balanced load.
T1 and T2 can be considered 1:1 ratio transformers.
T1 voltages and currents:
- Current flowing through a-b is 0.1 ampere
- Current flowing through c-d is 0.1ampere in the opposite direction.
- This results in zero voltage across a-b and c-d
Volt turns in T1 is zero under balanced condition, since current in windings flows opposite directions. R1 current through a-b is equaled by T1 from d-c, so ampere turns magnetizing core oppose. T1 has no flux in core, since volt-turns = zero T1 can be shorted from a-b or from c-d with no effect.
T2 voltages and currents:
- e-f has the same current as flows through c-d, c-d has the same as a-b, 0.1 ampere
- g-h must also have the same current as flowing through e-f
- R2 has equal current with R1, 0.1 ampere
- this means g-h has 10 volts, phase as shown
Ampere turns (flux density) in T2 is R2 current times turns. T2 core carries all the flux in a balanced voltage balanced current condition.
Real Transmission Line 4:1 Balun Unbalanced Voltage R1 top =0V
The same balun with perfect unbalance in load, top grounded:
In this case we have voltages as shown above. Notice now flux density in T2 is twice T1. T1 is now required to allow voltage at top of R1 to be zero. Shorting a-b or g-h would prevent proper operation.
Real 4:1 Transmission Line 4:1 Balun Bottom Grounded
Now we see flux density in T2 is zero.
- g-h or e-f can be shorted
- Flux density in T1 is maximum, flux in T2 is zero.
Single Core Dual Transmission Line Balun
It has been proposed a single core can be used with two 1:1 choke baluns in a transmission line balun and still provide a current balun. That cannot be true unless each transformer has IDENTICAL flux density.
Here's what happens to our balun above if we have a core that provides a closed path for all flux:
This is very simple transformer theory. If we have identical turns on each winding and if they are on a common core so all flux passes through each winding, EMF across each winding must be equal. This means any solution of voltages to the load must provide:
- The sum of voltages from c to e must equal supply voltage
- Output voltage across load is now 20v, so we have a correct 4:1 impedance ratio
- Load is voltage unbalanced, that means if we ground center tap or either end of the load we upset voltages and currents in the system. We no longer have a balun, we have an unbalanced voltage source.
Any tolerance of the three balance conditions a current balun must maintain would only occur if the core had flux leakage. The worse the core, the better the balun will behave.
Sevik proposed a transmission line balun like the balun above could be wound on a single core. That isn't true. A balun configured as above must be on two separate cores or it will not remain balanced.
Chris Trask's "Solution", is it a transmission line or a transformer?
Chris Trask, N7ZWY, recently claims to have built an improved 4:1 transmission line balun on a single core. Full details of his claims are at http://www.home.earthlink.net/~christrask/Trask4to1Balun.pdf
Trask calls this a transmission line balun, but is it? He and I will have to agree to disagree on that point. Even though we might disagree about names, it won't change how a balun works. It won't allow the Sevik TL 4:1 balun to work as a current balun on one core.
Analyzing Trask's circuit will show a common mistake those of us unfamiliar with transmission lines might make. For the purpose of discussion or analysis only, here are copies of the balun circuit appearing on Trask's page:
If we look at polarity of T1 (or T2) we see the same phase winding terminals of the "V" windings (notice the winding phase dots on T1 are reversed from normal) have identical polarities to the inputs at any instant of time. In an actual transmission line mode, the start or finish ends of T1 and T2 must be excited differentially. A transmission line is excited like this:
The source end of the transmission line must always be fed with equal and opposite currents, and must always have the source applied in differential across the line at the input (source end) only.
In a transmission line (excited as shown above) energy is conveyed from end-to-end in a TEM mode. This mode requires, under the conditions of matched load, voltage between conductors along the line to be in a precise relationship with current. In the case of a 50 ohm line with 50 watts, current (through vector) would be 1 ampere while voltage (across vector) would be 50 volts. This is true anywhere along the line.
If we mismatch the line, the product of voltage across and current through the line at any point is still 50, even though the ratio of E to I will change.
We have two conditions then that apply to any load.
In a matched condition voltage across and current through at any point are always in the same ratio, and that ratio equals line impedance and the product always equals power applied. Transmission currents in the two conductors are always exactly equal and opposite.
In a mismatched line the voltage across and current through the line at any point has a vector product equal to power applied, and the ratio of voltage and current at any point is equal to the line operating impedance at that point. Transmission currents are always equal and opposite.
Here is how Trask feeds his "transmission line":
He takes output from the conductor normally used as the opposing conductor in a transmission line. The electrical equivalent of his "transmission line" circuit is shown here:
This obviously is not a transmission line, but instead is a simple basic primary/secondary transformer.
Let's see if this system follows the same rules as a transmission line in TEM mode.
Notice in all cases above voltage across the line at any and all points is zero. This means no energy is conveyed along the line in TEM (transmission line) mode, even though currents are exactly equal and opposite. This system does follow the basic rules of a conventional transformer, in that the secondary ampere-turn product always equals primary-ampere turn product in order to keep secondary magnetic flux in equilibrium with primary flux density.
For example, if we have a lossless one turn primary and two turn secondary transformer with one ampere flowing in the primary, we know we must have 1/2 ampere in the two-turn secondary. This is independent of impedance between conductors.
Trask uses equal turns, and calls it a transmission line because conductors are concentric. The parallel conductors Trask calls a transmission line could be 100 ohms Z0, or 2 ohms Z0, and all voltage differentials and currents through the lines remain the same. The product of across and through vectors at any point along Trask's "transmission line" are zero, because it does not convey energy through TEM (transmission line) mode operation.
In TEM mode, in a matched condition, the across and through vectors (E and I) at any point multiply to give us power flowing past that point. In Trask's "transmission line", the same product is zero because voltage is zero. We can change line impedance, and we have very little effect on SWR! As a matter of fact there is no requirement we use a pair of 100 ohm lines to build a 4:1 200 ohm to 50 ohm balun in Trask's system, because capacitance across and inductance through the conductors does not compensate like it does in a TEM mode.
Let's look again at the exact circuit Trask used to build a "single core 4:1 transmission line balun" using the same connections but with transformers turned 90 degrees:
and the original Trask drawing:
We see these two circuits are precisely the same. The "new improvement" isn't an improvement or anything new at all. It is just a conventional isolation transformer balun, not a transmission line balun (at least according to the engineering definition a transmission line conveys energy via a TEM mode).
You might ask... What does this hurt? What's the big deal?
- Instead of energy being conveyed to the load by conduction currents flowing through a direct wired path (as in a transmission line balun), energy is now transferred through the "balun" via flux coupling between conductors. This means the balun core is involved in all energy transfer.
- The fact the core is directly subjected to magnetizing forces and is excited directly by source voltage greatly limits power/ mismatch range of the balun. A normal transmission line balun can tolerate extreme mismatches if proper materials are used, but the same size and quality materials in a transformer-style balun handle less power into matched loads, and significantly less power into highly mismatched loads.
- In a normal transmission line (even one used in a balun) the series inductance of the conductors is balanced by the shunting capacitance between the conductors. This means if we terminate the transmission line correctly, VSWR bandwidth is extremely wide.
A typical high power 4:1 transmission line balun I build has a 1.2:1 VSWR bandwidth from 300 kHz to over 100 MHz. Trask offers the following SWR curve in his article for his "improved balun":
A return loss of -20.8 dB would represent the 1.2:1 VSWR points in his return loss graph. You can see the peaky SWR response only falls below -20 dB (below 1.2:1) between perhaps 15 and 30 MHz (the exact numbers are hard to see), which is only a 2:1 frequency range. An actual transmission line balun operates with minimal SWR over a 300:1 or wider frequency range and has a very flat curve.
This doesn't mean Trask's "balun" (it's actually an isolation transformer) can't be used in many practical applications. It does mean, for given material, physical size, and cost, it will handle less power (because the core is subjected to full flux under all conditions of load balance) and has decreased SWR bandwidth when compared to a true transmission line balun.
since June 12 2005