# Lumped LC Balun

[Could not find the bibliography file(s)
Balun, stands for balanced to unbalanced, is a single ended to differential converter or viceversa. A lumped LC balun is realized using lumped components, two inductors and two capacitors is shown in Figure 1. It is also called “lattice type” LC balun. Though a lumped LC balun using discrete components on PCBs is very popular low cost solution for narrow band applications, still it had appeared on some RFICs [?].

### LC Balun Calculator

Figure 1. Schematic of discrete L-C balun

### Analysis

To get an insight into circuit and simplify the analysis, the schematic is redrawn as shown in Figure 2. If node Y is grounded, the circuit form single ended to differential converter from to . Instead if node ‘Z’ is grounded, it form differential  to single ended converter.

Figure 2. Discrete LC balun redrawn with floating nodes(no ground connection)

To simply analysis let us assume the circuit is operating at resonant frequency() where
By KVL around the loop-,

(1)

By KVL around the loop-,

(2)

By KCL at node-,

(3)

The input impedance of the circuit is

(4)

Therefore the characteristic impedance() of the LC-balun is given by

(5)

Ouput Voltage
From Figure 2, voltage at terminal of load w.r.t node Y is

(6)

From Figure 2, voltage at terminal of load w.r.t node Y is

(7)

From Eq.(6) and Eq.(7) we can state that the voltage signals at and terminals of the balanced load at not out-of-phase with each other. The signals will be out-of-phase only under the condition . If conversion is required over a frequency band around operating frequency it further degrades. Therefore the circuit has very limited bandwidth.

Differential voltage across load,

(8)

### Design Equations

Follow the steps below to design a discrete LC balun
1) Since it is a narrow band transformation, know your operating frequency
2) Find the impedance of reactive elements using the equation
3) Compute the values of inductor and capacitor. and

### Design Example

Example below shows how to calculate the values of L and C for a discrete balun to use as 50 to 200 single ended to differential converter at 900MHz operating frequency.

1) Given fo = 900MHz
2)
3) L =
4) C =

### Applications

1. Single ended to differential conversion or viceversa
2. Impedance transformation

### References

This site uses Akismet to reduce spam. Learn how your comment data is processed.