J

#### Jon Kirwan

- Jan 1, 1970

- 0

I'd like to consider the Vbe multiplier often used in audio

amplifiers to maintain a bias voltage for the output stage.

The purpose is to better mitigate against ripple in the

unregulated power supply rails and against the the VAS

voltage output resulting from amplified signal voltages.

(The only active device under consideration is a BJT, though.

No JFETs or MOSFETS or opamps or other ICs.)

The basic starting form for a Vbe multiplier is shown in Fig.

1 and the bias voltage output is indicated there. Assume Q1

is thermally coupled in some magic way, for now, in just the

right way so that if the current through the Vbe multiplier

were perfectly stable, that the bias voltage would track just

as needed (The 'Eg' of Q1 is exactly what's needed for the

output stage's temperature tracking in some nice way and the

values of R1 and R2 are set correctly and the thermal

coupling and location is somehow where it needs to be.) The

focus is on the Vbe multiplier's variation of bias in the

face of changes in sourcing current at the top of Fig. 1.

: +V

: |

: resistor or

: current source

: |

: ,---+---,

: | |

: \ |

: / R2 |

: \ +-----> upper quadrant

: / | ^

: | | |

: | |/c Q1 BIAS

: +-----| VOLTAGE

: | |>e |

: \ | |

: / R1 | v

: \ +-----> lower quadrant

: / |

: | |

: '---+---'

: |

: VAS ---'

:

: FIGURE 1

If I use a resistor as the load for the VAS, it's obvious to

me that the Vbe multiplier will need to cope with varying

currents. But even if I use a BJT (or two) to make a current

source sitting above the Vbe multiplier, it's still not going

to hold entirely still with +V ripple and with varying VAS

drive voltages. That variation will ultimately manifest

itself in a varying Vbe bias voltage. That will change the

operating point for the output stage.

If it is class-A, I suppose it doesn't matter that much. But

I don't want to be forced into class-A operation. Nor do I

want to be forced into regulated rails. So it becomes a

little more important, I think, to get this nailed down

better.

There's the problem, anyway.

To quantify how bad all this really is, I tried my hand at

figuring out the small signal analysis of the Vbe multiplier.

If I got a first approximation about right, it is based

squarely upon the small-re of the BJT. The very familiar

value for (kT/q)/Ic.

There is also the value of R2 shown in Fig. 1, but since its

effect is only affected by the change in base current, I

believe it's contribution is divided by Q1's beta. So the

actual equation is something like:

R_ac = (1/Ic)*(kT/q)*(1+R2/R1) + R2/beta

For a 2X multiplier where R2 is about R1, this is:

R_ac = (2/Ic)*(kT/q) + R2/beta

The Vbe multipler value is:

V_bias = Vbe*(1+(R2/R1)) + R2*Ic/beta

(The latter term being a correction for base current.)

Ignoring base current for now and assuming I had Ic set

around 5mA and placed R1=R2=1k for the 2X factor, this R_ac

value works out to about 15.4 ohms.

A variation of half an mA in Ic yields about 7.7mV change in

the bias point.

I decided to see if the Early effect made much of a

difference. The adjustment appears to be something like

this:

R_early = dV/dI = -Ic/VA*R^2

If I'm interpreting it right, it really does show as negative

resistance added to R_ac. The fuller equation, then,

including the Early effect, would be:

R_ac = (2/Ic)*(kT/q) + R2/beta - Ic/VA*R^2

(Which requires a quadratic solution to solve for R.)

If R_ac is 15.4 ohms and Ic is around 5mA, a VA of 100V would

suggest about R_early=-10mOhms. Which is roughly a factor of

1500 less than 15.4 Ohms. Since it now appears to be on the

order of 0.1% or so for typical Ic, VA, and, R_ac values, I

think I can ignore it for these considerations.

So drop it, I will.

I had scouted around a few weeks back (not for this reason)

and found what is shown in Fig. 2. I remembered it, but

didn't understand it then.

: +V

: |

: resistor or

: current source

: |

: ,---+---, <-- node A

: | |

: | \

: | / R3

: \ \

: / R2 /

: \ |

: / +-----> upper quadrant

: | | ^

: | |/c Q1 |

: +-----| BIAS

: | |>e VOLTAGE

: \ | |

: / R1 | v

: \ +-----> lower quadrant

: / |

: | |

: '---+---'

: |

: VAS ---'

:

: FIGURE 2

I think I now understand why R3 was there. Changes in Ic

create changes in Q1's collector voltage, per Ic*R3. The

result is that dV=dI*R3. If R3 is on the order of the above

computed R_ac, then variations at node A caused by changing

currents through the Vbe multipler (most of which are seen as

Ic changes) will be neatly compensated for the change in the

voltage drop caused by R3.

However, that can only be set for some assumed Ic. Nearby

changes will work pretty well. But further deviations will

start to show problems again. Also, the Fig. 2 version will

use a slightly higher multiplier value to get node A up high

enough for the R3 drop to hit the right place required to

bias the output stage. That higher multiplier means that

while, let's say, the two (or four, if that's it) output

BJT's Vbe values vary over temp and the thermally coupled Q1

above also varies it's own Vbe value, the multiplier other

than 2 (or 4) will mean the variation of the bias will match

at only one place -- if it ever did more than one spot. How

important that is, I've not considered yet.

I'm wondering about additional topology changes to improve

the performance still more. Obviously, if they are crazy and

wild, I'm probably going to live with the above and be done

with it. But I think there's got to be something still

better. Another BJT as a bypass route across Q1 and R3?

Getting this nailed down should help mitigate against both

unreg supply ripple (on one side, anyway) putting hum into

the output and also against large scale changes in the VAS

amplified signal voltage (which means distortion.)

Jon