Transistor biasing, Lecture-XIX and XX.

Transistor Biasing: Base resistor and Voltage divider bias.

Analog systems and applications — lecture-XIX & XX.

This article belongs to a series of lectures on analog electronics, the paper goes by the name “Analog Systems and Applications” for the physics honors degree class. All lectures of this series will be found here. This article consists of the 19th and the 20th lectures of the series. The lectures was delivered on 27th March 2018.

In the latest episodes of this series we discussed in fair detail and illustration the ideas of how two diodes can be combined to form bipolar junction transistors (BJT) that are capable of switching and amplification functions. We saw their characteristics in various configurations in our first two lectures (here). Then we discussed the 3 regions of operations in the BJT and discussed the special case of common base configuration in our 3rd lecture (here). In our last lecture (here) we discussed the load line analysis, Quiescent point and the 3 regions of operations, especially for the case of the common emitter configuration.

Now we would like to delve on the important basic concept of biasing a transistor. We have seen the details of biasing the diodes earlier (mainly here, and here, apart from in their applications in later lectures: such as various rectifiers, in LED and photodiodes and in Zener diode voltage regulator, you should assimilate exactly how the idea of biasing helps us achieve a wide variety of capabilities of the diodes).

Transistor Biasing.

Transistors operate as amplifiers when external DC supply voltages are used and a desired current I_C is produced. The control voltage or current are known as “BIAS”.

Usually we need two biasing DC sources, one in the input circuit and one in the output circuit. But this is inconvenient and costly. We can instead use only one supply bias voltage: V_CC.

There are various ways to achieve this type of biasing. Eg Biasing with (i) Base resistor (ii) Feedback resistor (iii) Emitter resistor (iv) Voltage divider

From among these four, we will discuss only (i) and (iv) ie. biasing with base resistor and voltage divider bias.

(i) Base resistor biasing.

This is also known as a “Base bias” or a “fixed bias” circuit.

• A single DC supply of voltage V_CC is applied to both collector and base wrt emitter.
• Emitter is the reference level of voltage i.e its considered “grounded” or “earthed”.
• A high value of resistance R_B (~ 100 kΩ or more) is connected between base and positive end of supply voltage V_CC for n-p-n type transistors. For p-n-p type transistors R_B is connected between base and negative end of supply voltage V_CC.

The following diagrams show the circuits for both n-p-n and p-n-p type of transistors in the common emitter configuration.

• “Zero signal” base current I_B can be achieved by selecting proper value of base resistor R_B. If I_C is “zero signal” collector current and β is the current gain, then; I_C = βI_B.
• Lets apply Kirchhoff’s law to the input loop, that is, base-emitter circuit. Then: V_CC = I_BR_B + V_BE ⇒ I_B = (V_CC – V_BE)/R_B. V_BE is very small compared to V_CC. eg V_BE is 0.3 V for Ge and 0.7 V for Si. We can neglect V_BE. Thus: I_B = V_CC / R_B.
• Supply voltage V_CC is fixed. Once R_B is selected, base current I_B is also fixed. This is the reason this mode of biasing is known as “fixed bias method”.
• Collector current in the output circuit is given as: I_C = βI_B + I_CEO, where I_CEO is the leakage current in the CE configuration. Although I_CEO is not as small as I_CBO, still a small error is entertained if I_CEO is neglected. So, I_C = βI_B.
• Lets apply Kirchhoff’s law to the output circuit (i.e. collector-emitter loop). V_CC = V_C + V_CE = I_CR_C + V_CE. ⇒ I_CR_C ≤ V_CC or I_C ≤ V_CC / R_C. Thus (I_C)_max = V_CC / R_C, is known as saturation collector current: (I_C)_saturation. It is independent of the base current I_B. In this situation: I_C = βI_B, is invalid.

How to determine operating point in fixed bias?

• Know V_CC, select R_B, I_B calculated: I_B = V_CC / R_B. If V_BE is known more precise equation: I_B = (V_CC – V_BE)/R_B can be used.
• I_C calculated from: I_C = βI_B (Using available transistor data for β). Its verified that I_C ≤ (I_C)_saturation (from I_C ≤ V_CC / R_C).
• V_CE is calculated from V_CC = I_CR_C + V_CE.

Advantage

• Circuit is very small, only 2 resistances and 1 battery are required. Only one resistance (R_B) fixes the operating point.
• No resistance is required across base-emitter junction.
• Biasing point and Q-point can be easily set by adjusting value of R_B.

Disadvantage

This type of circuit is not used very often, for following reasons:

• Operating point depends on β. When β is large, transistor operates in saturation region and linear amplification is not produced.
• Poor stabilization: Q-point varies due to individual variation (e.g. replacement of transistor with a different one) or thermal runaway (i.e. variation of temperature)
• Stability factor is very high. It indicates likelihood of thermal runaway.

(ii) Voltage divider biasing

• It is the most extensively used biasing method. The reason is it has a very high degree of bias stability even when β and leakage current are high.
• Two resistances R₁ and R₂ are connected across supply bias voltage V_CC as shown in the diagram below. R₁ and R₂ form a voltage-divider, the reason why this type of biasing is known as “voltage divider biasing”. Voltage drop across R₂, forward biases emitter diode, hence the name “emitter bias” or “self bias” are also used for these type of circuits.

• Lets apply voltage-divider rule in the input circuit to determine V₂ across R₂. eqn 1.
• Kirchhoff’s voltage law, in the base circuit gives V₂ = V_E + V_BE =I_ER_E + V_BE. eqn 2. Or, I_E = (V₂– V_BE) / R_E eqn 3.
• Kirchhoff’s (voltage) law applied to the output circuit : V_CC = V_C + V_CE + V_E = I_CR_C + V_CE + I_ER_E. eqn 4. I_C and I_E are approximately equal (since I_B << I_C). Thus; V_CC = V_CE + I_C ( R_C + R_E ). This gives: V_CE = V_CC – I_C ( R_C + R_E ) and I_C = (V_CC – V_CE) / ( R_C + R_E ).
• Thus β does not appear in any of the above equations. Operating point is independent of β of transistor. Replacement of transistor does not affect operating point.
• Effect of temperature change: Increasing temperature will increase I_C. This causes “voltage drop across emitter resistance R_E” to increase. But voltage drop across R₂ is independent of I_C. Thus V_BE must decrease. This increases I_B which in turn decreases I_C. This makes voltage divider bias circuit as a very suitable one for many applications.
• (I_C)_saturation = V_CC / (R_C + R_E). (V_CE)_cutoff = V_CC. DC load line has intercepts; vertical: V_CC / (R_C + R_E) and horizontal: V_CC.