1. FDP in air – Feeding the antenna Given 288Ω input impedance of FDP in air, a common feed strategy is 300 ohm twin-lead or ladder line transmission line. Let’s see if this works even with two parallel flat traces Equations available for two parallel cylindrical wires Since using flat trace and not cylindrical wires, use approximation (Balanis, p. 514): a e = 0.25*a Where a e = effective radius if cylinder, a = trace width Given existing feed point of FDP has feed gap of 60 mils and trace width of 20 mils, calculate Zo of transmission line Simulate a quarter-wave differential line Add differential line to FDP in air to see if still matches

2. FDP in air – Feeding the antenna (cont.)

3. FDP in air – Feeding the antenna (cont) To test if 333Ω is correct, let’s feed the antenna with a quarter wave (90°) line. Given a load of 288Ω, the impedance should be 385Ω at the end of the quarter wave transformer.

4. FDP in air – Feeding the antenna (cont.) 288 Ω 50 Ω 1205 mils 90° Simulate just the differential line to verify the Zo calculation and expected impedance at end of quarter-wave differential line It works! Momentum

5. FDP in air – Feeding the antenna (cont.) 50 Ω 1205 mils 90° Now with the antenna and the same quarter-wave differential line Not 385Ω at input anymore? Capacitance between lines and antenna? Momentum

6. Test board 1 Test board 2 LayerThickness (mils)Characteristics Top solder mask1.00 ε r = 3.8, tan δ = 0 Top1.24 σ = 5.81*10 7 S/m FR410.20 ε r = 3.7940, tan δ = 0.0183 Ground1.18 σ = 5.81*10 7 S/m FR436.52 ε r = 3.9920, tan δ = 0.0165 Vcc1.18 σ = 5.81*10 7 S/m FR410.20 ε r = 3.7940, tan δ = 0.0183 Bottom1.24 σ = 5.81*10 7 S/m Bottom solder mask1.00 ε r = 3.8, tan δ = 0 TOTAL63.8 On both boards, the FDP, feedlines, and layer stacking (~62 mil board) are identical. Test board 1 is for the balun measurement and board 2 is for the two-port measurement. L = 1757 mils w = 83 mils g = 59 mils d = 237.5 mils trace width = 20 mils 50Ω line 50Ω lines L w g d

7. Test boards 1 & 2: Balun and Two-port Measurements and Simulations Measurements Simulations Balun Two-port One internal port Two internal ports BW = 45MHz 62MHz 70MHz 63MHz 80-j*74Ω source