**Subject :**Microwave Engineering

**Unit :**Microwave tubes

## Limitations of conventional vacuum devices at microwave frequency

Conventional vacuum triodes, tetrodes, and pentodes are less useful signal sources at frequencies above 1 GHz because of lead-inductance and interelectrode-capacitance effects, transit-angle effects, and gain-bandwidth product limitations. These three effects are analyzed in detail in the following sections:

**Lead·lnductance and Interelectrode·Capacitance Effects :-
**

At frequencies above 1 GHz conventional vacuum tubes are impaired by parasiticcircuit reactances because the circuit capacitances between tube electrodes and the circuit inductance of the lead wire are too large for a microwave resonant circuit. Furthermore, as the frequency is increased up to the microwave range, the real part of the input admittance may be large enough to cause a serious overload of the input circuit and thereby reduce the operating efficiency of the tube. In order to gain a better understanding of these effects, the triode ciruit shown in Figure should be studied carefully

**Figure : Triode circuit (a) and its equivalent (b)**

Figure (b) shows the equivalent circuit of a triode circuit under the assumption that the interelectrode capacitances and cathode inductance are the only

parasitic elements. Since Cgp << Cgk and wLk << 1/(wCgk), the input voltage Vi. can be written as

..(1)

and the input current as

...(2)

Substitution of Eq. (1) in Equation (2) yields

The input admittance of the tube is approximately

in which ωL_{k}g_{m}<<1 has been replaced. The inequality is almost always true, since the cathode lead is usually short and is quite large in diameter, and the transconductance g_{m} is generally much less than one millimho.

The input impedance at very high frequencies is given by

The real part of the impedance is inversely proportional to the square of the frequency, and the imaginary part is inversely proportional to the third order of the

frequency. When the frequencies are above 1 GHz, the real part of the impedance becomes small enough to nearly short the signal source. Consequently, the output power is decreased rapidly. Similarly, the input admittance of a pentode circuit is expressed by :

where C_{gs} is the capacitance between the grid and screen, and its input impedance is given by

There are several ways to minimize the inductance and capacitance effects, such as a reduction in lead length and electrode area. This minimization, however, also limits the power-handling capacity.