Question

• • CP Cell phones that use 4G technology receive signals broadcast between 2 GHz and 8 GHz. (a) If you want to create a simple L-R-C series circuit to detect a 4.0 GHz cell phone signal, what is the relevant value of the product LC, where L is the inductance and C is the capacitance? (b) If you choose a capacitor that has C = 1.0 x 10–15 F, what inductance do you need? (c) Suppose you want to wind your own toroidal inductor and fit it inside a box as thin as your cell phone. Based on the size of your phone, estimate the largest cross-sectional area possible for this. (d) Assume the largest allowable radius of the toroid is 1.0 cm and estimate the lowest number of windings needed to create your inductor, assuming the material inside has a relative permeability of 1.

Answer 1

(a) The relevant value of LC is given by, 1 LC= 4л' 1 4m2 (4x10 Hz) 1 ir* (4x10) 4T24X -1.58x102 s Therefore, the relevant value of LC is 1.58x102 (b) From part(a) LC 1.58x 1021 s2 L1x1015 F) 1.58x102 s L 1.58x 10 H Therefore, the inductance is 1.58x 10 H (c) The largest cross sectorial area is given by, па? A 4

(10 m ( d-1cm) 4 0.78x10 m2 m2. Therefore, the required area is 0.78x 10 (d) The number of windings are given by, 2πη L(2nr) N2 (4Tx 10" ) (71) Lr 2a2 (1x10) Substitute the numerical values in the above equation (1.58x10)(1x10) N2 2x(10")(1x10) -0.25x10 N 50 Therefore, the number of windings are 50