What happens when bjt beta is infinity?
What happens when bjt beta infinity?

Nothing for well-designed circuits.

Beta, or the current gain of a BJT, can vary significantly between units of the same model.  Most datasheets tell you the minimum guaranteed gain at a few operating points, but usually don't spec a maximum gain.  Actual gain of a few parts in a batch can be 10x the minimum guaranteed gain.

Good circuits work with the transistors having from the minimum gain to infinite gain.  Fortunately, that's not hard to design to.  Making sure the circuit works with the minimum gain is usually the part you design to.  In most cases, more gain just works.

For example, consider a simple LED driver:



Let's say this is a typical green LED and drops 2.1 V.  Figure the transistor will drop 200 mV in saturation, so that leaves 2.7 V across R2 when the LED is on.  That means the current thru R2, and therefore the transistor's collector current, is (2.7 V)/(150 &Omega;) = 18 mA.

Figure 700 mV B-E drop, so that leaves 2.6 V across R1 when the digital output is high.  The transistor's base current is therefore (2.6 V)/(2.7 k&Omega;) = 960 &micro;A.

The minimum gain required of the transistor for this circuit to work as intended is therefore (18 mA)/(960 &micro;A) = 19.  What would happen if the transistor gain was 50 instead?  Nothing significantly different.  50 / 19 = 2.6, which means the transistor is getting 2.6 times more base current than needed to stay in saturation.  The C-E saturation voltage may be a little less than the worst case 200 mV figure we used to design the circuit with, but what exactly will that do?  The LED current will be very slightly higher.  Even if the transistor were a perfect switch and had 0 C-E voltage when on, the LED current would only be 19.3 mA instead of the 18 mA when assuming 200 mV saturation.  You wouldn't be able to see the resulting brightness difference, even in a side by side comparison.  There would be more brightness variation between LEDs from the same batch and due to temperature.

Analog circuits work similarly.  For common emitter amplifiers, the input impedance goes up with gain.  Whatever is driving the amplifier input already has to be able to drive the minimum impedance when the transistor happens to have its minimum guaranteed gain.  Driving a higher impedance is usually not a problem.

You can certainly contrive cases where too large a gain makes the circuit not work, but one criterion for good design with BJTs is that this not be the case.  Fortunately, this is usually not hard to achieve.