The Ideal Inverter:

Prior to examining the performance of bipolar transistor inverter, it is helpful to have knowledge of what the needs of an ideal inverter are. The gate is predicted to accept an input logic signal in defined voltage levels, invert it and give an output voltage to drive other gates as shown in figure below.

Figure: The Ideal Inverter

a) Logic Voltages:

logic HI  V_H = V_CC     
logic LO V_L = 0V 
If V_i < V_CC/2, V_O = V_H = V_CC
If V_i > V_CC/2, V_O = V_L = 0V

(b) Drive Capability:

Ideally I_SNK, I_SCE → ∞

V_O must be independent of load conditions

(c) Noise Immunity:

The output must be insensitive to noise superimposed on the input and must provide defined switching.

d) Switching Speed:

Ideally, there must be no switching delay however an instantaneous response of the output to a change at input.

Bipolar Transistor Switch:

Basically, the bipolar transistor switch shown in figure below functions in one or other of two states.

OFF state – Transistor in the Cut-Off mode.
ON state – Transistor in the Saturation mode.

Figure: A Simple Bipolar Transistor Inverter

Base resistor R_B, serves to control the level of base current. The collector resistor R_C, serves to limit the maximum collector current however acts basically as an output load for the transistor.

Figure below shows a set of output characteristics for the transistor as I_C vs. V_CE for the range of values of IB. The load line can be superimposed on such curves which states the operating path followed by the output of transistor for particular load resistor, R_C and supply voltage V_CC. This path is set up as follows:

Load line: I_C = (V_CC - V_CE)/R_C = - [(1/R_C) V_CE] + (V_CC/R_C); the equation of a straight line.

If I_C = 0 then, V_CE/R_C = V_CC/R_C => V_o = V_CE = V_CC

If V_CE = 0 then, I_C = V_CC/R_C = I_{C max}

Such points can be employed to plot the load line superimposed on the characteristic curves of transistor. Figures below show the contrast between operating the transistor as an amplifying device in forward active region and operating it as a logic switch where it consists of two states; either ON in saturation mode or OFF in the cut-off mode.

(i) Operation as an Amplifier:

Whenever operating in linear active region, base emitter junction is forward biased and the base collector junction is reverse biased. Beneath such conditions:

I_C = β_F I_B and V_o = V_CE = V_CC - I_CR_C

This can be seen that a small signal superimposed on base current is amplified to provide a much greater change on collector current. The variation in collector current, passing via the load resistor, R_C, transforms this into an output voltage signal. Note that, as the I_C rises, V_O reduces and vice-versa and for this reason the signal is inverted from input to output.

(ii) Operation as a Switch:

Whenever acting as a switch, the transistor operates exterior of the linear active region beneath steady-state conditions and only passes via it when changing the state. As a switch, the transistor functions either in cut-off region or the saturation region.

Cut-Off:
   
With V_i = 0,   V_BE = 0,   I_B = 0, then I_C = 0,   Transistor is OFF
   
Then V_O = V_CC – I_CR_C = V_CC
   
Therefore, with V_i = 0 = V_L   input L_O, we encompass V_O = V_CC = V_H output HI

This is the logic inverting action.

Saturation:

In linear active region, I_C = β_F I_B. Whenever using the transistor as a switch, the load resistor R_C, is employed as a current limiting resistor to limit the collector current to I_C = I_{C max} = V_CC/R_C. When a high base current is injected to the transistor in such a way that:

β_F I_B >> I_CMAX   that is, I_B >> I_CMAX/ β_F

Then the transistor can’t amplify the base current, I_B, since the potential resultant current can’t flow in the collector, as the collector current is restricted to I_{C max}. In this case, the transistor can’t carry on executing in the forward active region and is driven into saturation region. Here with:

V_i = V_cc , I_B = (V_CC - V_BE)/R_B  then I_C = I_CMAX = (V_CC - V_CESAT)/R_C

The Transistor is ON and V_o = V_{CE SAT} → 0 usually 0.1 – 0.2V

Hence with,

V_i = V_CC = V_H input HI we have, V_O = V_CESAT = V_L output LO
 
This is as well as logic inverting action.

In saturation, the base of transistor is stated to be overdriven. That is to state more current is fed into the base than is needed to produce the maximum current which can flow in the collector. Usually, 4 to 5 times the current required to bring the collector current to IC max is injected to the base to guarantee that it is overdriven and the transistor executes in the saturation mode.

Figure: Operation of the Bipolar Transistor as an Amplifier

Figure: Operation of the Bipolar Transistor as a Switch

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