Electronics and Communication - Formula Sheet

Semiconductor and Transistor Formulas

• Energy Gap: \(E_g = E_c - E_v\) (where \(E_c\) is conduction band energy and \(E_v\) is valence band energy).
• Transistor Current Relation: \(I_E = I_B + I_C\) (where \(I_E\) is emitter, \(I_B\) is base, and \(I_C\) is collector current).
• Common Emitter Current Gain: \(\beta = \frac{\Delta I_C}{\Delta I_B}\) (the ratio of change in collector current to base current).
• Common Base Current Gain: \(\alpha = \frac{\Delta I_C}{\Delta I_E}\) (the ratio of change in collector current to emitter current).
• Gain Relation: \(\beta = \frac{\alpha}{1 - \alpha}\) or \(\alpha = \frac{\beta}{1 + \beta}\).

Oscillator and Communication Formulas

• Resonant Frequency: \(f = \frac{1}{2\pi\sqrt{LC}}\) (where \(L\) is inductance and \(C\) is capacitance).
• Antenna Range: \(d = \sqrt{2Rh}\) (where \(R\) is Earth's radius and \(h\) is antenna height).
• Line of Sight Distance: \(d_{max} = \sqrt{2Rh_T} + \sqrt{2Rh_R}\) (where \(h_T\) and \(h_R\) are transmitter and receiver heights).
• Signal Bandwidth: \(BW = \nu_2 - \nu_1\) (where \(\nu_2\) is upper and \(\nu_1\) is lower frequency limits).

Logic Identities

• De Morgan's First Theorem: \(\overline{A + B} = \overline{A} \cdot \overline{B}\) (complement of sum equals product of complements).
• De Morgan's Second Theorem: \(\overline{A \cdot B} = \overline{A} + \overline{B}\) (complement of product equals sum of complements).