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  Dynamic Characteristics I and Switching Times

Switching Times:

In practice, modifications in the state of conduction of transistor take time to take place. This cause delays in the response of output to changes at the input. Let consider a circuit as shown in figure below:

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Figure: Non-Instantaneous Switching in the Transistor Inverter

Figure below exhibits the series of events throughout turn-on and turn-off of the transistor. The following characteristic switching times can be recognized.

Delay Time, td

This is the delay between switching on input base current to transistor and the point at which the transistor reaches cut-in and enters the forward active mode. Throughout this time, the transistor is not truly conducting however ionization currents are flowing that essentially charges up the base-collector and base-emitter junction capacitances. The length of this duration is generally quite small as compared with the other switching times and can be ignored.

Fall-Time, tf

Note that the fall-time for output voltage is, however, the rise time of collector current. Throughout this time, the transistor is operating in forward active mode, passing between saturation and cut-off. Note that the collector current reaches its utmost value at the edge of saturation, even although the charge stored in the base of transistor continues to increase as the transistor is overdriven into heavy saturation. The fall-time is generally estimated between 90% and 10% points on the output voltage profile.

Storage-Time, ts

It is the time between the point at which the input voltage is brought low and that at which the output voltage starts to increase or correspondingly, the point at which the collector current starts to drop. Throughout this time, the transistor is still in saturation region. Therefore the collector current remains at its maximum saturation value, IC MAX, throughout this time. In effect what is happening is that the volume of surplus minority charge stored in the base, that has been put in by overdriving the transistor, is being eliminated through the base resistor till the transistor reaches the edge of saturation and enters the forward active region over again. Very frequently, the storage time is the biggest of the switching times and might be the principal limiting factor in the speed of operation of transistor in the digital circuits.

Rise-Time, tr

Note that the rise-time for output voltage is, however, the fall-time of the collector current. Throughout this time, the transistor is again operating in forward active mode passing between the edge of saturation and cut-off. The collector current drops from its maximum value towards zero. Note, as well, that during this time, the base current is negative as surplus minority charge carriers are being eliminated from the base region. The rise-time is generally measured between 10% and 90% points on output voltage profile.

The Ebers Moll model is an excellent large-signal, steady-state transistor model. Though, it does not deal with the transient conditions of modifying charge carrier profiles during modifications of mode of operation of the transistor whenever it is turning on or off. A better model is required to take account of such dynamic conditions.

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 Figure: The Sequence of Events during Transistor Switching

BJT Charge Control Model:

Remember the minority carrier concentration profile in base region of a bipolar npn transistor operating in the forward active mode as shown in figure below:

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Figure: Minority Carrier Charge Profile in the Base Region of BJT

Collector Current:

The profile of charge distribution can be approximated as linear, that means that the slope of the distribution is taken as steady. This is equivalent to neglecting recombination in the base region and supposing that all electrons diffuse via base into the collector region. When the hole component of the collector current is ignored, it can then be state that the collector current is directly dependent on the volume of charge in base region in the forward active mode, QF, and the forward transit time, ΤF, for electrons passing via this region. Then beneath steady-state conditions:

IC ≈ QF/ΤF, That is equal to αF = 1
         
When the linear approximation is supposed to extend to dynamic conditions where the volume of charge in base is changing, then for instantaneous collector current:

iC(t) = QF(t)/ΤF  and diC(t)/dt = (1/ΤF) [dQF(t)/dt]

That is to state that, changes in the collector current will directly follow modifications in the surplus minority charge stored in the base whenever the transistor is operating in the forward active mode.

Base Current:

The base current is composed beneath steady-state conditions of the recombination component and the hole currents across the junctions. Recombination component can be evaluated as the volume of charge in base divided by the minority carrier lifetime:

IBR = QF/ΤB

The hole currents can be accounted for by taking a modified equivalent carrier lifetime ΤBF = βF ΤB to provide a simplified steady-state base current of:

IB = QF/ΤBF

When the base terminal is employed as an input or controlling terminal, as in the case of single transistor inverter, then any modification in the base charge will be due to the change in base current. Involving a time varying component for dynamic conditions then provides the instantaneous base current as:

iB(t) = QF(t)/ΤBF + dQF(t)/dt

Emitter Current:

Finally, for the emitter current, iE = iB + iC, and hence:

IE(t) = QF(t)/ΤF + QF(t)/ΤBF + dQF(t)/dt

The complete model of charge control should as well account for the charge stored in the junction capacitances and modifications in such charges are as shown in figure below. These are designated QBC and QBE for base-collector and base-emitter junctions correspondingly. Dynamic changes in such charges will give mount to additional components of currents as dQBC/dt and dQBE/dt.

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Figure: Currents due to Changing Charges in the Junctions of BJT

The ultimate complete set of Charge Control Equations for Forward Active mode of operation of the Bipolar Junction Transistor is then provided as:

iC = QF(t)/ΤF – dQBC(t)/dt

iB = QF(t)/ΤBF + dQF(t)/dt + dQBC(t)/dt + dQBE(t)/dt

iE = QF(t)/ΤF + QF(t)/ΤBF + dQF(t)/dt + dQBE(t)/dt

In a more complicated charge control model, such equations can be extended to comprise the reverse mode of operation of transistor as well; however this is not essential for our purposes.

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