**BJT Cutoff Frequency and Capacitance:**

**Device Cutoff Frequency –** All transistors have junction capacitances. The junction capacitances and the transit time of charge carriers through the semiconductor material limit the high frequency performance of the device. This limitation is expressed as a **cutoff frequency** (f_{α}), which is the frequency at which the transistor current gain falls to 0.707 of its gain at low and medium frequencies. The BJT Cutoff Frequency and Capacitance can be expressed in two ways,

**the common emitter cutofff frequency f**_{αe}, and**the common base cutoff frequency (f**_{αb}).

f_{αe} is the frequency at which the common emitter current gain (h_{fe}), falls to 0.707 x (mid-frequency h_{fe}). f_{αb} is the frequency at which the common base current gain (h_{fb}) falls to 0.707 x (mid-frequency h_{fb}). It can be shown that,

Equation 8-7 shows that f_{αb} can be identified as the current-gainbandwidth product, or total bandwidth (f_{T}). This is the designation used on many transistor data sheets. The data sheet portion in Fig. 8-6 shows that f_{T} is 250 MHz for a 2N3903 and 300 MHz for a 2N3904.

**Junction Capacitances:**

As already discussed, all BJTs have BJT Cutoff Frequency and Capacitance. These are identified as the base-collector capacitance (C_{bc}) and the base-emitter capacitance (C_{be}), (see Fig. 8-7). The device data sheet portion in Fig. 8-8 shows that the capacitances are usually listed as an output capacitance (C_{obo}l, which is the same as C_{bc}, and an input capacitance (C_{ibo}) which corresponds to C_{be}. It should be noted that in both cases, the capacitance values are specified for reverse-biased junctions with zero current levels. C_{obo} varies when V_{CB} is altered, however, the changes are usually a maximum of approximately ±3 pF. C_{ibo} changes substantially from the specified capacitance when the base-emitter junction is forward biased, (as it always is for linear BJT operation).

When an emitter current flows across the BE junction, there is a diffusion capacitance at the junction. This is directly proportional to the current level. It can be shown that,

**Miller Effect:**

Figure 8-9 shows an input signal (+ΔV_{i}) applied to the base of a transistor connected in CE configuration. If the circuit voltage amplification is -A_{v}, then the collector voltage change is,

Note that, because of the phase reversal between input and output, the collector voltage is reduced by (A_{v} ΔV_{i}) when the base voltage is increased by ΔV_{i}. The increase in V_{B} and decrease in V_{C} results in a total collector-base voltage reduction of,

This voltage change appears across the collector-base capacitance. Using the equation Q = C x ΔV, it is found that the charge supplied to the input of the circuit is,

Therefore, “looking into” the base, the collector-base capacitance appears to be (1 + A_{v})C_{bc}. So, the capacitance is amplified by a factor of (1 + A_{v}). This is known as the **Miller effect**.

The total input capacitance (C_{in}) to the transistor is (1 + A_{v})C_{bc} in parallel with the base-emitter capacitance (C_{be});

It should be noted that the Miller effect occurs only with amplifiers that have a 180° phase shift between input and output, (an inverting amplifier). Consequently, it occurs with CE circuits, but not with CB and emitter follower and circuits.