**High Frequency Limitations:**

As stated, transistors suffer from High Frequency Limitations. These are of a twofold nature. On the one hand, there are the same difficulties as those encountered with tubes, On the other hand, there is some difficulty in specifying accurately the performance of microwave transistors in a manner which would make it relatively easy for the equipment designer to use them.

**Limitations:**

If one has become familiar with the limitations of vacuum tubes at High Frequency Limitations, it is relatively easy to predict the limitations of transistors. Thus, capaciÂtances between electrodes play an important part in determining high-frequency response. Both current gains, Î± and Î², eventually acquire reactive components which make both complex at first and eventually unusable. Interelectrode capacitances in bipolar transistors depend also on the width of the depletion layers at the junctions, which in turn depend on bias. The situation is somewhat more complex than with tubes, whose interelectrode capacitances are not so bias-dependent. The difficulty here is not that the transistor has a poorer high-frequency response; quite the opposite. It is simply a greater difficulty in finding parameters with which to describe the behavior so as to give a meaningful picture to the circuit designer.

Electrode inductances have more or less the same nuisance value as with tubes, but since transistors are smaller, electrode leads are shorter. Thus suitable geometry and the use of low-inductance packages go a long way toward reducing the effects of lead inductance.

The effect of transit time is identical to that in tubes, although its actual operation is somewhat different. The smaller distances traveled in transistors are counterbalanced by the slower velocities of current carriers, but overall the maximum attainable frequencies are somewhat higher than for tubes. In traveling across a bipolar transistor, the holes or electrons drift across with velocities determined by the ion mobility [basically higher for germanium (Ge) and gallium arsenide (GaAs) than silicon (Si)] the bias voltages and the transistor construction. We first find majority carriers suffering an emitter delay time, and then the injected carriers encounter the base transit time, which is governed by the base thickness and impurity distribution. The collector depletion-layer transit time comes next. This is governed mainly by the limiting drift velocity of,, the carriers (if a higher voltage were applied, damage might result) and the width of the depletion layer (which is heavily dependent on the collector voltage). Finally, electrons or holes take some finite time to cross the collector, as they did with the emitter.

**Specification of Performance:**

Several methods are used to describe and specify the overall High Frequency Limitations behavior of RF transistors, Older specifications showed the alpha and beta cutoff frequencies, respectively f_{Î±b}Â and f_{Î±c}.Â The first is the frequency at which Î±, the common-base current gain, falls by 3 dB, and the second applies similarly to Î², the common-emitter current gain. The two figures are simply interconnected. Since we know that

It follows that, for the usual values ofÂ Î²,

These frequencies are no longer commonly in use. They have been replaced by f_{T}, the (current) gain-bandwidth frequency. This may simply be used as a gain-bandÂwidth product at low frequencies or, alternatively, as the frequency at which Î² falls to unity, i.e., the highest frequency at which current gain may be obtained. It is very nearly equal to f_{Î±b}Â in most cases, although it is differently defined.

Up to a point, f_{T} is proportional to both collector voltage and collector current and reaches its maximum for typical bipolar RF transistors at V_{ce}Â = 15 to 30 V and I_{c} in excess of about 20 mA. This situation is brought about by the higher drift velocities and therefore shorter transit times corresponding to the higher collector voltage and current.

Finally, there is one last frequency of interest to the user of microwave transistors. This is the maximum possible frequency of oscillation, f_{max}. It is higher than F_{T}Â because, although Î² has fallen to unity at this frequency, power gain has not. In other words, at Î² = 1 output impedance is higher than input impedance, voltage gain exists, and both regeneration and oscillation are possible. Although the use of transistors above the beta cutoff frequency is certainly possible and very often used in practice, the various calculations are not as easy as at lower frequencies. The transistor behaves as both an amplifier and a low-pass filter, with a 6 dB per octave gain drop above a frequency whose precise value depends on the bias conditions.

To help with design of transistor circuits at microwave frequencies, scattering-(S) parameters have been evolved. These consider the transistor as a two-port, four-terminal network under matched conditions. The parameters themselves are the forward and reverse transmission gains, and the forward and reverse reflection coefficients. Their advantage is relatively easy measurement and plotting on the Smith chart.