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4.2 Impedance and Admittance 163 4.2.4 Admittance & Parallel Elements When connecting circuit elements in parallel it may be advantageous to use admittances instead of impedances. The admittance is defined as the inverse of the impedance. ( ) If you compare eq. (4.2-1) with (4.2-3) you can see two major differences. Firstly the moduli of admittance and impedance are the inverse of one another. Secondly, whilst the angle of the impedance represents the difference between the phases of voltage and current ( ), the angle of the admittance represents the difference between the phases of current and voltage ( ). In a Cartesian form the admittance may be written as Where the real part is termed conductance and the imaginary part is termed susceptance. Now let us consider the parallel R-C circuit shown in Figure 4.2-19. Figure 4.2-19 Parallel R-C circuit, voltage and current waveforms at 1000 MHz Following a similar procedure to that used in the R-C series case, from the markers in the rectangular frames in Figure 4.2-19 we may write | | The SI units of admittance are Siemens, expressed by the capital letter S. Nonetheless milli Siemens, mS, are generally easier to handle and simplify calculations. This is because the ratio of current in and voltage in , directly gives . Now consider the markers in circular frames in Figure 4.2-19, which show us the time interval by which current leads the voltage. Remembering that (section 1.5.4.2) and that we are in a sinusoidal steady state at a frequency of 1000 MHz, we may write 0 0.5 1 1.5 2 Time (ns) parallel_R_C -1 -0.5 0 0.5 1 -60 -30 0 30 60 p2 p1 1.257 ns 0.999 V 1.079 ns 40.5 mA 0.5 ns 0 V 0.3323 ns 0 mA Vtime(M_PROBE.VP1,1)[*] (L, V) parallel_R_C Itime(ACVS.V1,1)[*] (R, mA) parallel_R_C p1: Freq = 1000 MHz p2: Freq = 1000 MHz Freq = 1000 MHz (4.2-3) Conquer Radio Frequency 163 www.cadence.com/go/awr

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