Clapp oscillator). Practical example Fig. 3 shows a working example with component values. Instead of bipolar junction transistors, other active components such as field-effect transistors or vacuum tubes, capable of producing gain at the desired frequency, could be used. The capacitor at the base provides an AC path to ground for parasitic inductances that could lead to unwanted resonance at undesired frequencies. Selection of the base's biasing resistors is not trivial. Periodic oscillation starts for a critical bias current and with the variation of the bias current to a higher value chaotic oscillations are observed. Theory One method of oscillator analysis is to determine the input impedance of an input port neglecting any reactive components. If the impedance yields a negative resistance term, oscillation is possible. This method will be used here to determine conditions of oscillation and the frequency of oscillation. An ideal model is shown to the right. This configuration models the common collector circuit in the section above. For initial analysis, parasitic elements and device non-linearities will be ignored. These terms can be included later in a more rigorous analysis. Even with these approximations, acceptable comparison with experimental results is possible. Ignoring the inductor, the input impedance at the base can be written as where is the input voltage, and is the input current. The voltage is given by where is the impedance of . The current flowing into is , which is the sum of two currents: where is the current supplied by the transistor. is a dependent current source given by where is the transconductance of the transistor. The input current is given by where is the impedance of . Solving for and substituting above yields The input impedance appears as the two capacitors in series with the term , which is proportional to the product of the two impedances: If and are complex and of the same sign, then will be a negative resistance. If the impedances for and are substituted, is If an inductor is connected to the input, then the circuit will oscillate if the magnitude of the negative resistance is greater than the resistance of the inductor and any stray elements. The frequency of oscillation is as given in the previous section. For the example oscillator above, the emitter current is roughly 1 mA. The transconductance is roughly 40 mS. Given all other values, the input resistance is roughly This value