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What's the difference between a balun and a 180-degree hybrid (such as a rat-race coupler)? This is not a joke, it is a serious question... both provide paired, equal-amplitude outputs (or inputs) that are 180 degrees apart. There a few differences... A 180-degree hybrid includes at least one isolation resistor such that the outputs are somewhat isolated. A balun does not. Also, a balun (usually) converts unbalanced signal to a balances signal. The Tsai balun breaks this rule. On a 180 hybrid, all of the ports are unbalanced.
The subject network was published in the 1990s, by M.C. Tsai. It employs a pair of Lange couplers hooked up so that they provide 180 degrees between two equal-amplitude ports. In the original paper, the network was on GaAs, presumably the author was working on mixers at the time (at Uncle Ray's Rest Camp). Nowadays, MMIC mixers are dominated by Analog Devices and Maury, while Tsai's employer has moved on, to high-volume defense products such as phased arrays using GaN.
Here is another gentleman from the 1990s, with initials "M.C.". we do not know if M.C. Tsai also wore parachute pants...
Can't Touch This
Below is a schematic of a Tsai balun we created on 15 mil alumina. The interconnect lines are all equal in length and width, except for the open circuit port of the lower Lange. We let the optimizer rip on certain parameters, subject to constraints, to determine things like optimum line width and spacing of the coupled strips. The final values for strip width and gap are 20um and 28um respectively. In Tsai's paper, he allowed the two couplers to have different strip gaps. We found that this did not make a huge difference in performance to we made them identical. With fewer things to keep track of in circuit layout, you'll have a lower probability of making a mistake... We used 0.015nH for the inductance of the ground via on the left, it's probably not accurate but if we were going to build this circuit, we'd model the entire thing in a 2.5D EM design tool like Axiem.
Tsai Balun Model\
Here's a little trick for optimizing something. Put it inside a circuit as a subcircuit, and optimize the top-level circuit.... here, we called it "Tsai balun optmizer".
Tsai Balun Optimizer schematic
Let's look at the optimized response. If you allow 10 dB return loss, it works from 5 to 15 GHz, a remarkable 100% bandwidth!
Tsai Balun Optimizer S-parameters
Now let's plot the data on the balun by itself. The optimizer lines are gone. This is what you will present at a design review or in a paper. Don't give away how you actually optimized it. You will prevent some manager derailing the meeting byasking "what are those lines for?"
Tsai Balun Spars
Nexr, let's look at isolation between port 2 and 3. Whoops, it really stinks. Why? Because there is no isolation resistor! So, it is indeed a balun, by our definition and not a 180-degree hybrid.
Tsai Balun Isolation
Here are some equations for defining the phase of the balun. How many times have you seen a stupid plot of 180-degree phase shift where it flips between -180 and +180 degrees, so you can't really see what is going on? Or worse, someone plots S21 angle and S31 angle on the same plot, with axes ticks at 50 degrees (should be 45, right?) so that the reader has to do the subtraction in their head.
Tsai Balun Equations
Here the phase difference is plotted, nicely. Please take a pledge to only plot phase difference this way. M.C. Tsai did it correctly in his paper in case you were wondering.
Tsai Balun Phase
Now let's move the important parameters to "global definitions" so they can be reused by other circuits...
Finally, let's look at one of the consituent couplers. Here the global parameters are used, so that you can sleep well knowing that its geometry is identical to that of the couplers in the balun.
Tsai Lange Model
As Tsai pointed out, the ideal response is slighty undercoupled. By "undercoupled" we mean that the coupled port (purple trace) has lower amplitude than the direct port (red trace). It is far easier to make someting under-couple than over-couple.
Tsai Lange S-parameters
Reference
M. C. Tsai, "A new compact wideband balun," IEEE 1993 Microwave and Millimeter-Wave Monolithic Circuits Symposium Digest of Papers, 1993, pp. 123-125.