9.2 Baluns, Ununs, and Common-Mode Current Choking

9.2 Baluns, Ununs, and Common-Mode Current Choking

An antenna system consists not merely of the radiating wire or tubing in the air, but of the entire electromagnetic assembly comprising the transmitter, feedline, matching transformers, and ground environment. A persistent source of station dysfunction—manifesting as distorted radiation patterns, inexplicable RF feedback in the radio shack, unexplained high noise floors, and RFI complaints from neighbors—stems from improper interfacing between balanced and unbalanced circuits. Resolving these challenges requires mastering the physics of baluns (balanced-to-unbalanced transformers), ununs (unbalanced-to-unbalanced transformers), and common-mode current chokes.

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Balanced vs. Unbalanced Transmission Systems

To understand why baluns are necessary, we must examine the electromagnetic field geometry of balanced versus unbalanced lines.

   Balanced System (e.g., Open-Wire Ladder Line)      Unbalanced System (Coaxial Cable)
          +I  ------------------------------>               +I_center -------------------->
                                                                      [ Dielectric Core ]
          -I  <------------------------------               -I_inner  <===================
              (Equal currents, opposite phase,                        (Shield Inside Surface)
               identical impedance to ground)               +I_outer  ~~~~~~~~~~~~~~~~~~~>
                                                                      (Shield Outside - Common Mode!)

1. Balanced Systems (Dipoles, Loops, Open-Wire Feeders)

A balanced system is electrically symmetrical with respect to ground. In a center-fed half-wave dipole or a two-wire open ladder line:

• Both conductors exhibit identical physical dimensions and identical stray capacitance to surrounding earth and structures.
• The alternating voltages on the two conductors are equal in magnitude and $180^\circ$ out of phase ($V_1 = -V_2$).
• The RF currents flowing along the conductors are equal in magnitude and flow in opposite directions ($I_1 = -I_2$).
• Because the conductors carry equal and opposite currents in close proximity, their external radiated fields cancel completely along the transmission line, preventing the feedline from radiating.

2. Unbalanced Systems (Coaxial Cable)

A coaxial cable is an asymmetrical, unbalanced transmission line:

• The central conductor is entirely enclosed within a cylindrical conducting shield.
• The shield is maintained at ground potential at the transceiver chassis.
• Forward signal current flows along the center conductor ($I_{\text{center}}$).

The Skin Effect and the Three-Conductor Reality of Coaxial Cable

At radio frequencies ($> 1.8\text{ MHz}$), electrical currents do not penetrate uniformly through a conductor. The skin depth ($\delta$) in copper is defined by:

$$\delta = \sqrt{\frac{\rho}{\pi f \mu}}$$

where $\rho$ is copper resistivity ($1.724 \times 10^{-8}\ \Omega\cdot\text{m}$), $f$ is operating frequency, and $\mu$ is permeability ($4\pi \times 10^{-7}\ \text{H/m}$). At $14\text{ MHz}$, the skin depth is approximately $17\ \mu\text{m}$ ($0.017\text{ mm}$). Because standard coaxial braid is several skin depths thick:

1. The Inner Shield Surface: Carries the return current ($I_{\text{inner}}$) for the center conductor. Guided by electromagnetic boundary conditions within the dielectric, $I_{\text{inner}}$ is strictly equal and opposite to $I_{\text{center}}$ ($I_{\text{inner}} = -I_{\text{center}}$). The net magnetic field outside the inner shield surface is zero.
2. The Outer Shield Surface: Acts as a separate RF-current path, largely isolated from the inside by skin effect; real shielding still permits some coupling. Current flowing on the outside of the shield is termed common-mode current ($I_{\text{cm}}$). It flows unimpeded along the exterior of the cable jacket and radiates into free space exactly like an unguided wire antenna.

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Direct Coax Connection and the Common-Mode Path

When a coaxial cable is connected directly to a center-fed dipole without an isolation device:

• The center conductor connects to antenna leg A.
• The shield connects to antenna leg B.

Coax center ----------------o A ---- Antenna leg A

Coax shield interior -------o B ---- Antenna leg B
                            |
Shield exterior <-----------+
       Possible common-mode path along cable exterior

A and B are separate feed terminals.
Desired differential current returns inside the shield.

At this junction, antenna leg B connects directly to two parallel paths:

1. The inside surface of the shield (guided return path back to the generator).
2. The outside surface of the shield (path to ground via the cable exterior).

Antenna asymmetry or the feedline's coupling to its surroundings can drive current on the shield exterior. Its magnitude depends on the impedance of the complete common-mode return path.

Define $I_A$ and $I_B$ as phasor currents directed away from the feed terminals into the two legs, and $I_{\text{cm}}$ as the exterior current directed away from the feedpoint. Current balance gives $I_{\text{cm}}=-(I_A+I_B)$. For balanced differential operation, $I_A=-I_B$ and the exterior current is zero. A finite exterior current indicates imbalance.

Possible Consequences of Common-Mode Current

1. Pattern Changes: The feedline exterior can radiate, filling nulls or changing lobes and front-to-back ratio. There is no universal direction or amount of takeoff-angle change.
2. RF in the Shack: Exterior current can reach chassis and connected cables, causing audio distortion, computer-interface faults or RF burns.
3. Receive Noise: By reciprocity, noise coupled onto the exterior can reach the antenna feedpoint and receiver. The noise change depends on local sources and coupling; it is not a fixed decibel increase.

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Balun Topologies: Voltage Baluns vs. Current Baluns

A balun interfaces a balanced antenna or line with an unbalanced feed. Voltage and current baluns impose different ideal conditions; practical suppression depends on their construction and the connected load.

Voltage balun: ideal V_A = -V_B relative to the reference.
Unequal impedances to the reference can give unequal leg currents.

Current balun: ideal I_A = -I_B.
A practical choke adds finite impedance to the common-mode path.
Differential flux cancels ideally; common-mode flux remains.

1. Voltage Baluns (Ruthroff Type)

A voltage balun is wound as an autotransformer or trifilar transformer on a toroidal core. Its winding topology forces the potentials at the two balanced output terminals to be equal and opposite relative to ground:

$$V_1 = -V_2$$

Voltage Balance and Current Imbalance

The antenna legs may have different impedances to their surroundings. In a simplified leg-to-reference model,

$$I_A=\frac{V_A}{Z_A},\qquad I_B=\frac{V_B}{Z_B}.$$

Even with $V_A=-V_B$, unequal $Z_A$ and $Z_B$ generally give $I_A+I_B\ne0$. Thus voltage balance alone does not ensure current balance or suppress exterior shield current. Reactance alone does not imply imbalance: both complex impedances and their symmetry matter.

A voltage transformer has core excitation set by its winding voltage, frequency, turns and core properties. Excess flux or loss can cause distortion and heating. Neither load imbalance alone nor a universal $400\text{ W}$ threshold determines saturation.

2. Current Baluns (Guanella Transmission Line Type)

A current balun (first developed by G. Guanella in 1944) treats the winding as a transmission line (a bifilar pair or miniature coaxial cable) wound through one or more high-permeability ferrite toroids.

Operational Principle: The Common-Mode Choke

A current balun adds impedance to the common-mode path while allowing the wanted differential signal through its transmission line:

• Differential Mode: Equal and opposite conductor currents ideally produce cancelling flux in the surrounding core. The line still has conductor/dielectric loss and voltage/current limits.
• Common Mode: Exterior shield current, or same-direction current on a wire pair, produces core flux. It encounters a complex choking impedance $Z_{\text{cm}}=R_{\text{cm}}+jX_{\text{cm}}$, which depends on frequency and construction.

High common-mode impedance reduces the imbalance current. In the ideal limit,

$$I_A=-I_B.$$

A real choke has finite impedance, so residual common-mode current can remain. Its resistive component dissipates $I_{\text{cm}}^2R_{\text{cm}}$; excessive excitation can overheat the core. Current baluns are useful for maintaining current balance with asymmetric antenna surroundings, but their suppression and power capability must be assessed for the intended bands and duty cycle.

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Specific Balun Configurations and Impedance Ratios

1:1 Current Balun (Choke Balun)

A 1:1 current balun provides no intended differential impedance transformation. It can use a bifilar line or coax wound through ferrite cores and is commonly placed at a dipole, inverted-V or Yagi feedpoint. Select the material, dimensions and winding from measured choking-impedance data for the required bands. A turn count or material name alone does not establish full-HF coverage or a fixed decibel reduction.

4:1 Current Balun (Guanella Design)

A 4:1 Guanella balun transforms a $50\ \Omega$ unbalanced coaxial input to a $200\ \Omega$ balanced output. It is constructed from two identical 1:1 Guanella transformers:

• The inputs of the two transmission lines are connected in parallel ($50\ \Omega$ system input).
• The outputs of the two transmission lines are connected in series ($200\ \Omega$ balanced output).
• Because $(2 \times V)^2 / R$ yields an impedance transformation of $1:4$, it provides a true wideband $4:1$ step-up.
• Applications: Balanced antennas whose measured feed impedance is suitable for transformation to the coax impedance. A $200\ \Omega$ resistive load transforms to $50\ \Omega$ with an ideal 4:1 unit; height, geometry and surroundings determine the actual antenna impedance.

Use the correct winding polarity and adequate, reasonably matched common-mode impedances in both line sections. These are RF transmission-line-transformer connections, not two isolated ordinary transformers.

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Ununs: Unbalanced-to-Unbalanced Transformers

An unun transforms impedance between unbalanced ports. An end-fed antenna also needs an RF return, such as a counterpoise or another defined return path. An impedance-transforming unun alone does not necessarily suppress common-mode current on the coax.

9:1 Unun (Impedance Step-Down for End-Fed Wires)

A 9:1 unun utilizes a trifilar winding connected as an autotransformer on a ferrite toroid:

• Turns Ratio: The primary winding has $N$ turns, and the total winding has $3N$ turns (turns ratio $1:3$).
• Impedance Ratio: Impedance scales as the square of the turns ratio:

$$\frac{Z_{\text{secondary}}}{Z_{\text{primary}}} = \left(\frac{N_{\text{sec}}}{N_{\text{pri}}}\right)^2 = \left(\frac{3}{1}\right)^2 = 9:1$$

• Application: End-fed wire antennas can present high, complex impedances that change with frequency, wire length, height and the RF return path. For a specified $450+j0\ \Omega$ load at one frequency, an ideal 9:1 step-down gives $50+j0\ \Omega$. More generally, it gives $Z_{\text{in}}=Z_{\text{load}}/9$: it scales reactance as well as resistance rather than cancelling it. Measure the installed system and check the tuner's actual matching range.

4:1 Unun

A 4:1 unun uses a bifilar autotransformer to match $50\ \Omega$ coax to $12.5\ \Omega$ (stepping up low-impedance vertical mobile whips) or to match $50\ \Omega$ coax to $200\ \Omega$ unbalanced feeds (such as high-impedance ground planes).

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Coaxial Common-Mode Chokes: Coiled Coax vs. Ferrite Sleeves

Amateur operators frequently attempt to suppress common-mode shield currents using one of two methods:

Air-core coiled coax              Ferrite common-mode choke
Inductance + stray capacitance    Complex permeability + stray C
Frequency-selective impedance     Resistive loss can broaden response
Both have self-resonances; check impedance over the required bands.

1. Air-Core Coiled Coax ("Ugly Balun")

Coiling coax adds common-mode inductance, while inter-turn capacitance creates self-resonance. The impedance is inductive below a simple parallel resonance, high near resonance and capacitive above it. Such chokes are often more frequency selective than a suitably designed resistive ferrite choke. Useful coverage depends on the actual coil and surrounding common-mode circuit; it is not fixed to exactly one amateur band.

2. Ferrite Core Chokes (The W2DU and Toroidal Chokes)

1. Toroidal Choke: Pass the complete transmission line through ferrite cores, often with multiple turns.
2. Bead Choke: Pass the coax through a series of ferrite sleeves.

Ferrite has complex permeability, $\mu=\mu'-j\mu''$. Its loss component can produce a useful resistive choking impedance and damp resonance. Ferrite chokes still have parasitic capacitance and self-resonances. Their impedance curves depend on mix, dimensions and winding; more than one choke may be needed for wide coverage. A high resistive component is often useful because it does not cancel a reactive return path. Actual current reduction depends on the choke and the complete common-mode loop.

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Step-by-Step Worked Common-Mode Choke Calculation

An amateur transmitter generates $V_0 = 141.4\text{ V RMS}$ ($400\text{ W}$ into $50\ \Omega$). Due to antenna installation asymmetry, a common-mode RF potential of $V_{\text{cm}} = 100\text{ V RMS}$ is induced at the feedpoint between the shield exterior and local earth ground. The stray ground-return path impedance along the outside of the coax shield is measured as $Z_{\text{path}} = 50 + j20\ \Omega$ ($|Z| \approx 53.9\ \Omega$).

Step 1: Calculate Common-Mode Current WITHOUT a Choke

$$I_{\text{cm}} = \frac{V_{\text{cm}}}{Z_{\text{path}}} = \frac{100\text{ V}}{53.9\ \Omega} \approx 1.855\text{ A RMS}$$

This large exterior current could cause substantial unwanted radiation, interference or RF burns, depending on its distribution and the surrounding installation.

Step 2: Insert a High-Performance Guanella Current Choke

A 1:1 Guanella ferrite choke presenting a purely resistive common-mode choking impedance of $Z_{\text{choke}} = 4000\ \Omega$ is installed directly at the feedpoint.

The total common-mode loop impedance becomes:

$$Z_{\text{total}} = Z_{\text{choke}} + Z_{\text{path}} = (4000 + 50) + j20 = 4050 + j20\ \Omega$$ $$|Z_{\text{total}}| = \sqrt{4050^2 + 20^2} \approx 4050.05\ \Omega$$

Step 3: Calculate Suppressed Common-Mode Current

$$I_{\text{cm, suppressed}} = \frac{100\text{ V}}{4050\ \Omega} \approx 0.0247\text{ A RMS} = 24.7\text{ mA RMS}$$

Step 4: Calculate Attenuation in Decibels

$$\text{Atten (dB)} = 20 \log_{10}\left(\frac{I_{\text{unsuppressed}}}{I_{\text{suppressed}}}\right) = 20 \log_{10}\left(\frac{1.855}{0.0247}\right) = 20 \log_{10}(75.1) \approx 37.5\text{ dB}$$

With the assumed fixed $100\text{ V RMS}$ common-mode source and unchanged return path, the calculated reduction is $37.5\text{ dB}$ and the remaining current is $24.7\text{ mA RMS}$. This does not guarantee elimination of RFI or a particular receive-noise improvement. The choke also dissipates $I^2R\approx(0.0247)^2\times4000=2.44\text{ W}$ from this common-mode current, which its thermal design must accommodate.

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Comparison Table: Balun and Unun Classifications