Bipolar Junction Transistor -BJT AC Load Line Analysis Solved Examples

BJT Load Line & Q point Analysis: Complete tutorial with solved examples. Explain ac load line with respect to BJT. Transistor Load Line Analysis

DC load line

Variation of Q point and voltage swing limitations

Variation of Q point with different circuit parameters

In the previous section, I discussed the DC load line. There is an AC load line as well. The purpose of the AC load line is similar to its DC counterpart. It gives all possible values of ic and vce of a given amplifier. It also determines the magnitude of output voltage.

Fig 1 Base bias circuit

Fig 2 AC equivalent of the circuit in fig 1

The purpose of this section is to draw the AC load line:

The DC load line is drawn between two extremes that are the saturation point and the cut-off point. The AC saturation and cut off points are different from their counterpart DC load line. The Q point is common to both the load-lines. 

This is a little bit confusing for beginners, but I tried to make it easier. As you know Q point is calculated when no signal is applied to the input. When an input is applied the AC quantities (ic and vce) vary above and below Q point. 

AC saturation point: (ic(sat))

Fig 3: AC quantities vary above and below Q point

Look at AC equivalent circuit. 

rC = RC || R1

ic =  vce / rC

∆IC =  ∆VCE / rC

OR

∆IC = ( VCEQ - vce)/ rC

Substitute vce = 0 for saturation point on y-axis 

∆IC = VCEQ / rC

From fig 3

ic(sat) = ICQ + ∆IC

Substitute ∆IC, and we get AC saturation point ic(sat)

ic(sat) = ICQ + VCEQ/rC … equation 1

Note: Equation 1 shows the upper limit of the signal swing

AC Cutoff Voltage: (vce(cut-off))

vce  = iC*rC

∆VCE = ∆IC*rC

∆VCE = (ICQ -iC)*rC

Substitute iC = 0 , for cutoff point on x-axis

∆VCE = ICQ*rC

From fig 3 

vce(cutoff) = VCEQ + ∆VCE

Substitute ∆VCE, and we get AC cutoff point vce(cutoff)

vce(cutoff) = VCEQ + ICQ*rC … equation 2

Note: Equation 2 shows the lower limit of the signal swing

Fig 4

AC Output Compliance:

What does an AC load line do? It usually describes the AC output compliance of a given amplifier. With the help of the AC load line, we can determine the maximum peak to peak unclipped output voltage. Output voltage clips, if the output compliance exceeds. 

By adjusting the Q point in the middle of the load line, we can get the maximum possible peak to peak unclipped output.

 

It is determined by the maximum peak to peak collector current IC and VCE with respect to Q point. 

The maximum possible transition for vce with respect to Q point is shown in figure 1(b), which is ∆VCE.

∆VCE = ICQ*rC

For peak to peak value, multiply by 2.

PP = 2ICQ*rC

Where,

PP = output compliance

Maximum possible transition for ic(sat) with respect to Q point is shown in figure 1(a), which is ∆IC.

∆IC = VCEQ / rC

For peak to peak value, multiply by 2.

PP = 2∆IC = 2VCEQ / rC

Where,

PP = output compliance

Fig 5 signal swings and different Q points

Example:

Fig 6

Consider the same circuit. Q point values have been calculated in the previous article. 

ICQ= 3.1 mA

VCEQ = 3.8 V

Calculate AC cut off and saturation.

ic(sat) = ICQ + VCEQ/rC

rC = RC || R1 = 666.667 ohms

ic(sat) = 3.1m + 3.8/666.66

ic(sat) = 3.1m + 5.7m

ic(sat) = 8.8 mA

vce(cutoff) = VCEQ + ICQ*rC

vce(cutoff) = 3.8 + 3.1m*666.6

vce(cutoff) = 3.8 + 2

vce(cutoff) = 4.8 V

Fig 7

Conclusion:

For a given amplifier, the AC load line intersects the DC load line at the Q point. 

The steeper the AC load line, the smaller will be the output voltage swing.

The results obtained in equation 1 and equation 2 are in terms of the Q point of the given amplifier.

What is next?

In the next post, you will learn about the Q point location on the load line.

• Centred Q point
• Q point near saturation
• Q point near cut off

After a complete understanding of this topic, you will be able to design an amplifier.