In a series-fed Hartley oscillator, the frequency of oscillation is determined by the inductance and capacitance in the circuit, typically expressed by the formula:
[ f = \frac{1}{2\pi\sqrt{L(C_1 + C_2)}} ]
where ( L ) represents the inductance and ( C_1 ) and ( C_2 ) are the frequency-determining capacitances. When the capacitance is increased, the term ( (C_1 + C_2) ) in the denominator becomes larger, which inversely affects the frequency. Consequently, increasing the frequency-determining capacitance will lead to a decrease in the oscillator frequency.
This fundamental relationship indicates that with higher capacitance, the circuit requires a longer time to complete an oscillation cycle, thereby resulting in a lower frequency of oscillation. Understanding this relationship helps in designing and adjusting oscillators for specific frequency outputs in various applications.