MAGNETRON AS GENERATOR OF CENTIMETER WAVES 207 



plication of any external driving force. It is the sort of oscillation the circuit 

 would undergo were it left to itself after being excited or started initially. 

 Such an oscillation, once started, does not continue indefinitely because the 

 energy put into the circuit initially, dissipates itself in resistive losses in the 

 circuit components and in a load which may be coupled electromagnetically 

 to the circuit. The exponential rate at which the original energy is dis- 

 sipated is a very important characteristic of the circuit. It is usually 

 specified by a parameter Q, defined as lir times the ratio of the energy stored 

 in the circuit to the energy dissipated per cycle of the oscillation.^* Thus a 

 circuit always loses a certain fraction of its energy per cycle independent 

 of how great this energy may be. In the exponential decay of oscillations 

 in a resonator from which the drive has been removed, Q/Itt is the num- 

 ber of cycles of oscillation, required for the stored energy to decay to 1/e of 

 its initial value. Similarly, in the buildup of oscillations in a resonator 

 to which is fed a constant amount of energy per cycle, Q/2t is the number 

 of cycles required for the stored energy to buildup to (1 — 1/e) of its final 

 equilibrium value. 



It is possible to define several types of Qs for a circuit, depending upon 

 the nature of the energy dissipation being considered. If one considers 

 only the energy lost in the resistance of the circuit components themselves, 

 one defines the so-called unloaded Q, Qo. If the circuit is coupled electro- 

 magnetically to a resistive load, the Q defined in terms of the energy dis- 

 sipated in the load and internal resistance is called the loaded Q, Ql. 

 Finally, for some purposes it is convenient to consider the ratio of energy 

 stored to that dissipated in the external load only. This defines the ex- 

 ternal Q, Qext. It is clear that both Ql and Qexi are functions of the degree 

 of coupUng between the oscillating circuit and the resistive load. 



The Q parameters, however, tell one more than the rate at which energy 

 is dissipated in a circuit oscillating at its natural frequency. The admittance 

 of the circuit, measured as a function of the frequency of an external driving 

 source, passes through a minimum at the natural frequency of oscillation of 

 the circuit. The shar|3ness of the dip in the admittance curve is determined 

 by the Ql of the circuit in such a manner that the sharper the dip, the higher 

 the Ql. In passing through resonance the susceptance of the circuit changes 

 sign from inductive for frequencies below the frequency of resonance, to 

 capacitive, for frequencies above the frequency of resonance. The rate at 

 which the susceptance varies with frequency is another measure of the 

 sharpness of resonance and of the Ql of the circuit. 



5.4 Energy Storage and Loss: The remaining ideas concerned with a 

 simple L-C circuit of lumped constants which should be mentioned here are 

 the characteristic admittance of the circuit, the energy storage capacity, 



" As will be seen in the subsequent discussion the factor 2ir is included here so as to 

 simplify the definition in terms of admittance. 



