### Ohm's Law & the Power Equation

Ohm's Law is one of the most basic equations in electrical engineering, showing how voltage (\(V\)) is directly proportional to current (\(I\)) via the impedance (\(Z\)) of the circuit: \[ \begin{align} V &= I\cdot Z \tag{1} \\ I &= \frac {V}{Z} \tag{2} \\ Z &= \frac{V}{I} \tag{3} \end{align} \] Along with Ohm's Law, we have the Power Equation that relates the voltage (\(V\)) and current (\(I\)) to the power (\(P\)): \[ \begin{align} P &=V\cdot I \tag{4} \\ V &=\frac {P}{I} \tag{5} \\ I &=\frac {P}{V} \tag{6} \end{align} \] In order to relate the power (\(P\)) to impedance (\(Z\)), substitute equation (1) into (4): \[ \begin{align} P &=I^2\cdot Z \tag{7} \\ I &=\sqrt{\frac {P}{Z}} \tag{8} \end{align} \] and then substitute (2) into (4): \[ \begin{align} P &=\frac {V^2}{Z} \tag{9} \\ V &=\sqrt{P \cdot Z} \tag{10} \end{align} \] This is simple enough when the units are linear, but EMC commonly uses the logarithmic versions of these quantities. Before showing how Ohm's Law is implemented with logarithmic quantities, a brief review of the decibel is in order.### Decibels & Logarithms

In electrical engineering, the decibel is defined as a power ratio: \[ P(dB)=10\cdot log_{10}(\frac{P_2}{P_1}) \tag{11} \] and as we can see from equations (7) and (9) above, power is proportional to the*square*of the voltage or current: \[ \begin{align} dBW &\propto 10\cdot log_{10}(\frac{V_2}{V_1})^2 =20\cdot log_{10}(\frac{V_2}{V_1}) \tag{12} \\ dBW &\propto 10\cdot log_{10}(\frac{I_2}{I_1})^2 =20\cdot log_{10}(\frac{I_2}{I_1}) \tag{13} \\ \end{align} \] This definition is the reason that, when converting to \(dB\) equivalents of voltage and current, \( 20\cdot log_{10} \) is sometimes used instead of \( 10\cdot log_{10} \). With that in mind, the following are the definitions of converting voltage and current from linear to logarithmic units: \[ \begin{align} dBV &= 20\cdot log_{10}(\frac{V_2}{V_1}) \tag{14} \\ dBA &= 20\cdot log_{10}(\frac{I_2}{I_1}) \tag{15} \end{align} \] Return to the RF Calculator.