Series regulator circuit and stability factor

A series regulator keeps the output dc voltage constant when the input voltage or the load changes. The control element (pass transistor) is in series with the load, and an error amplifier compares a sample of the output with a Zener reference.

Circuit diagram

 Vi o----+-------------------+
         |                   | C
        [R]           B +----|  Q1 (pass)
         |              |    | E
         +--------------+    +------+---------+-----o Vo
         |                          |         |
         | C                       [R1]      [RL]
    Q2   |--B------------------+    |         |
         | E                   |    |        GND
         |                     +----+
        (Dz) Vz                     |
         |                         [R2]
         |                          |
        GND                        GND

Connections: Q1's collector goes to Vi and its emitter to Vo (an emitter-follower pass element). R, from Vi, supplies the base current of Q1 and the collector current of Q2. Q2's collector is connected to the base of Q1, its emitter is held at Vz by the Zener Dz, and its base is connected to the mid-point of the divider R1-R2 across Vo.

Operation

If Vo tends to rise, the base of Q2 rises, so Q2 conducts more and diverts current away from the base of Q1. Q1 conducts less, and Vo falls back. The opposite happens when Vo falls.

Output voltage

VB2 = Vo R2/(R1 + R2) = Vz + VBE2

Vo = (Vz + VBE2)(1 + R1/R2)

Stability factor (line regulation factor)

The stability factor S = ΔVo/ΔVi tells how much the output changes for a change in input.

Vo depends only on Vz and VBE2. When Vi changes, the base of Q1 stays at about Vo + VBE1, so the current in R changes by about ΔVi/R. This extra current flows through Q2 into the Zener, and its dynamic resistance rz turns it into a change in Vz:

ΔVz ≈ ΔVi · rz/(R + rz) ≈ ΔVi · rz/R

Taking VBE2 as constant (it changes only with temperature, by about −2 mV/°C):

ΔVo = (1 + R1/R2) ΔVz

S = ΔVo/ΔVi ≈ (1 + R1/R2) · rz/(R + rz)

Because rz is small (a few ohms to tens of ohms) compared with R (hundreds of ohms to kΩ), S is very small. For example, rz = 10 Ω, R = 1 kΩ and R1 = R2 give S = 2 × 10/1010 = 0.0198, about 2 % (20 mV per volt of input change). The regulation is improved by feeding the Zener from the regulated output, or by using a constant-current source in place of R.

For the simple Zener-follower series regulator (Vo = Vz − VBE), S = ΔVo/ΔVi ≈ rz/(R + rz).