This article explains the operation of a balun that transforms an unbalanced antenna structure into a balanced one. Simple and intuitive models of balanced and unbalanced structures are presented and the formation of a sleeve (bazooka) balun is detailed. The operation of the balun is explained using the transmission line theory.
Balanced and Unbalanced Half-Wave Dipole Antenna
Consider the ideal half-dipole antenna, shown in Figure 1. It is assumed that the medium surrounding the antenna is free space, free of obstacles and extending to infinity in all directions.
Under these assumptions, this ideal antenna is an inherently balanced structure. The sinusoidal current 
F at any point on the upper arm is the same in magnitude as the current R at the corresponding position on the lower arm (same distance from the RF voltage source). This ideal case assumes that are no other metallic, or conducting objects in the vicinity of the antenna, so the “forward” conduction current F is the same in magnitude as the displacement current D, which in turn in the same in magnitude as the “return” conduction current R.
If there are any metallic, or conducting objects (ground) in the vicinity of the antenna, this balance condition is violated, as illustrated in a simplified model shown in Figure 2. The forward current, F, upon leaving the upper arm returns to the source through several paths, only one of them being the lower antenna arm.
The magnitude of the current in the upper antenna arm is no longer equal to the magnitude of the lower arm current, IR = ID1 ≠ IF. The antenna structure is no longer balanced.
Now, let’s consider another ideal balanced antenna structure shown in Figure 3. The half-wave dipole antenna is connected to an RF source via a coaxial cable.
Again, let’s assume that the medium surrounding the antenna is free space, free of obstacles and extending to infinity in all directions. Also, let’s assume that the forward current travels from the RF source on the inner coax conductor, then through the upper antenna arm, continues as a displacement current, and returns on the lower antenna arm and the coax shield conductor to the source. The forward and the return currents are equal in magnitude and the antenna structure is balanced.
If there are any metallic or conducting objects (ground) in the vicinity of the antenna, this balance condition is violated, in a similar manner as shown earlier in Figure 2. For the structure shown in Figure 3 to be balanced, the entire return current must travel on the inner surface of the shield, as shown in Figure 4.
If any part of the return current is allowed to flow on the outside surface of the shield (current R2 in Figure 5), then some of this current will return to the source through a parasitic capacitance as a displacement current (current DR in Figure 5). This results in an unbalanced structure and unwanted radiation.
The unwanted current on the outside of the shield, R2, and subsequently the displacement current DR, are in effect the common-mode currents. This is shown in Figure 6.
Sleeve (Bazooka) Balun
The usual way of addressing this unbalance due to a coaxial cable is the use of a balun, which is an acronym for balanced to unbalanced. By using a balun we can transform an unbalanced structure into a balanced one.
The intent of the balun is to increase the impedance to ground seen by the outside shield current, and thus to minimize (ideally eliminate) the outer shield current. Thus, ideally, the return current in the lower antenna arm would equal the return current on the inside of the shield.
A common balun for the coax – dipole antenna structure is a sleeve or bazooka balun shown in Figure 7.
The sleeve length is λ/4 and it is grounded to the outer shield surface at its perimeter as shown in Figure 7 (point D). The upper arm of the dipole antenna is connected to the inner coax conductor (point A). The lower arm is connected to the inside of the shield conductor (point B).
With such connections, a transmission line is created where the sleeve constitutes one conductor and the outside of the coax constitutes the other conductor of the transmission line. This transmission line is short-circuited at one end, as shown in Figure 8.
To explain the effectiveness of the sleeve balun we need to review some transmission line theory.
Input Impedance to the Transmission Line
Consider the transmission line of length L, shown in Figure 9.
The transmission line is driven by a sinusoidal source and is terminated by a complex impedance 
L. The characteristic impedance of the line is ZC.
The input impedance to the line at the input to the line is [1],
(1)
where the phase constant β is related to the wavelength λ by
(2)
Let’s assume that the line length is λ/4, and the line is terminated with a short as shown in Figure 10. (Note that this is the same configuration as the sleeve balun shown in Figure 8).
Now the input impedance to this quarter-wavelength line terminated in a short is
(3a)
or
(3b)
Thus, the input impedance of the quarter-wavelength transmission line terminated by a short is infinite. This means that no current will flow into this transmission line, as shown in Figure 10.
Quarter-Wavelength Sleeve Balun
Since the quarter-wave long transmission line terminated with a short creates an infinite impedance at its input, all current flows on the inside surface of the shield. This is shown in Figure 11. This structure now becomes balanced.
Sleeve (bazooka) baluns are the narrow-band baluns since they work well only at the frequency where their length is one-quarter wavelength.
There are many other types of baluns; they all attempt to prevent (choke) the common-mode current from flowing on the outside of the shield. One such alternative is a ferrite toroid choke balun shown in Figure 12.
Recall that (ideal) in a common-mode choke, the self-inductance of each winding is equal to the mutual inductance between the windings, i.e., L = M The impedance seen by the differential mode current in each winding (F, R) is [2]
(4a)
The impedance seen by the common mode current, CM in each winding is
(4b)
Thus, in an ideal case, the choke is transparent to the differential mode currents and blocks the common mode currents. Ferrite-core baluns provide a high common mode impedance over a broader frequency range.
References
- Clayton R. Paul, Introduction to Electromagnetic Compatibility, Wiley, 2006.
- Bogdan Adamczyk, Foundations of Electromagnetic Compatibility with Practical Applications, Wiley, 2017.
