Choosing bias current for a BJT

[Dan Moos]

Assuming power draw isn't a major concern (for the sake of argument), what criteria is used to choose the bias current of a BJT?

I often see in book examples various apparently arbitrary currents chosen, but surely there is a "zone" where the transistor is best setup for the job.

I'm currently experimenting with a discreet Gilber Cell mixer I've built up. Just seeing how changing various parameters effects the output.

The example I'm working off of has about 4.5 mA of current for the whole circuit. This allows about 2.2  mA for each transistor in the "tail" transistors, and about 1.1 for each of the 4 transistors in the 2 diff pairs. How do I go about choosing these currents? Is there something in the datasheet I should be looking at? I'm using 3094s, but I'm asking the question generically.

[JoeyG]

look at the data sheet for the  where the transistor is characterised  - Hfe (current gain) at various Ic  ~  Pick the typical (middle)  Ic  and then you can calculate the  Ib     Ib~Ic/Hfe  then you have Ib.

Ib is the current in the into the base.      an Rb  that will give  this Ib     Rb = V(Rb)-0.65 /Ib    where V(Rb) is the available voltage across Rb .

Here's an LTSpice model of a Gilbert Cell
https://github.com/buttercutter/gilbert_cell_mixer

[Konkedout]

I'm using 3094s,

Do you mean 2N3904 or MMBT3904 (I am not differentiating between these two which are electrically similar but one is TO-92 and the other is SOT-23.  I am wondering if you swapped digits.)

I have been using these part numbers for long enough; to me it is as obvious as someone being 10 feet 5 inches tall instead of 5 feet 10 inches tall.

But I am not an expert on Gilbert cells.  The 2N3904 ought to work very nicely with collector current in the range of a few mA.  One thing to be concerned with is curves of transition frequency versus collector current.  So that will depend on the transistor.

If you want to operate at even lower current, consider something like MMBT5089.

[T3sl4co1l]

Mainly impedance and matching, then noise figure, and bandwidth.  But it depends, and any one of these may take priority.  A tuned RF amp for example might not need much bandwidth (and can make up any impedance high or low with matching networks), but a wideband amp has no choice but to use low impedances; and noise figure curves tend to favor surprisingly low currents, which can make wideband low noise designs problematic.

An active nonlinear / bilinear block like a mixer, will see these vary with operating condition, and during a cycle, so the nonlinearities must be managed for the application.  The input nodes can have fixed (source) impedance, and the collectors can have fixed (load) impedance, but the middle (C to E) node(s) have impedance inversely proportional to instantaneous current (r_e ~ Vth / Ie) which ultimately limits bandwidth.  Additionally, the noise factor at the inputs and outputs will matter, if that's a concern.

Tim

[Picuino]

The small-signal BJT equivalent model changes depending on the bias current. The equivalent emitter resistance is equal to Vt/Ic.
Where Vt = 26mV @ 300 Kelvin
Where Ic = collector current

For example for 4mA of collector bias current, the equivalent small-signal emitter resistance is 6.5 Ohms and the base voltage to collector current gain of the transistor will be 0.154mA/mV.
If you increase the collector bias current to 13mA, the equivalent small-signal emitter resistance will be 2 Ohms and the base voltage to collector current gain of the transistor will be 0.5mA/mV. Much higher.

[CaptDon]

In R.F. amplifiers you could choose class A, B, AB, AB1, AB2 or C. This could describe a base bias current anywhere from zero up to maximum expected collector current divided by 2, and then divide that number by HFE. The sweet spot depends a lot on the surrounding circuit and function the transistor is performing.

[wasedadoc]

look at the data sheet for the  where the transistor is characterised  - Hfe (current gain) at various Ic  ~  Pick the typical (middle)  Ic  and then you can calculate the  Ib     Ib~Ic/Hfe  then you have Ib.

Ib is the current in the into the base.      an Rb  that will give  this Ib     Rb = V(Rb)-0.65 /Ib    where V(Rb) is the available voltage across Rb .

Here's an LTSpice model of a Gilbert Cell
https://github.com/buttercutter/gilbert_cell_mixer

Hfe has a wide tolerance so a single base bias resistor is less appropriate when the collector current is to be closely set.  Better to use the three resistor scheme.  Two to set the base voltage and the third one in the emitter.