# Lumped LC Balun

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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 [?].

### 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.

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

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