Vocademy
Signal Gain

# Signal gain

## BJTs

Signal gain with BJTs is simpler than with FETs, so we will cover that first. When a small current is sent into the base of a bi-polar junction transistor a larger current flows into the collector. The question is how much larger. In a BJT the ratio of the base current compared to the collector is called hFE[1]. Notice that the "h" is lowercase and the "FE" is uppercase. This means that the parameter is for DC operation. For AC operation the equivalent parameter is called hfe (lowercase "fe").

hFE is the ratio of collector current to base current:

 hFE  = IC ————— IB

Where:

 hFE = Collector current to base current ratio. IC = Collector current, current flowing into the collector IB = Base current, current flowing into the base

This formula means that to find the collector current, multiply the base current by hFE.

IC = hFEIB

For example, if an NPN transistor has an hFE of 50 and 1 mA of current flows into the base, 50 mA will flow into the collector.

The collector current of a BJT has a fairly linear relationship to the base current. If we change the base current by a certain percentage the collector current will change by about the same percentage[2]. For this reason Bi-polar junction transistors are said to be current controlled or to amplify current.

The hFE is not an absolute value. It differs depending on the collector current and the collector-to-emitter voltage. A data sheet for a particular transistor will list several values for hFE, each for a different collector current and collector-to-emitter voltage combination.

The AC equivalent of hFE, called hfe. On transistor datasheets it is usually listed under the title of "Small Signal Gain". This the ratio of the change in collector current to the change in base current. Here is the formula that defines hfe:

 hfe  = ΔIC ————— ΔIB

Where:

 hfe = Ratio of change in collector current to change in base current ΔIC = Change in collector current (delta IC) ΔIB = Change in base current (delta IB)

Where hFE tells us how much collector current we will get with a certain base current, hfe tells us how much the collector current will change if we make a change in the base current.

ΔIC = hfeΔIB

For example, if an NPN transistor has an hFE of 50, and 2 mA of current flows into the base, 100 mA will flow into the collector. If we increase the base current to 3 mA we get a collector current of 150 mA. We increased the base current by 1 mA and the collector current increased by 50 mA. Therefore, this transistor not only has an hFE of 50 but also has an hfe of 50. The values of hFE and hfe are usually pretty close to each other. However, because hFE is different for different amounts of collector current, hfe will differ slightly from hFE.

### Beta

Sometimes the ratio of collector current to base current is called beta (β). However, this is not an industry standard and literature is inconsistent on the definition. Most sources say that beta is identical to hFE. Some say that beta is the AC gain and that hFE is the DC gain. Transistor data sheets typically avoid using the term "beta" and strictly use hFE to describe DC gain and hfe to describe AC gain.

### Alpha

Alpha (α) is another parameter you may come across. Alpha is the ratio of the emitter current to the collector current. Notice in the diagram above that the current that flows into the base flows out the emitter along with the collector current; the emitter current is the sum of the collector current plus the base current (recall Kirchhoff's Current Law). The base current is usually quite small compared to the collector current, so alpha is typically a small value. Alpha is useful when working with common-base amplifiers (discussed in Analog Circuits).

## Darlington pairs

Frequently, super-high current gains are required with BJTs. For example, a power transistor may require 100 mA of base current to deliver 5 amps of collector current (where the hFE is 50). However, the circuit "driving" the transistor may be only able to deliver 50 mA. The answer to this problem is a darlington pair.

 Schematic symbol for an NPN Darlington pair

In a darlington pair, the emitter of a low-power transistor feeds the base of a high-power transistor. In the above case, the 50 mA available from the driving circuit is more than enough to cause the low-power transistor to deliver 100 mA to the base of the power transistor. Darlington pairs can be made from any pair of BJTs. You can also obtain Darlington pairs manufactured together in a single package.

To find the gain of a darlington pair multiply the hFE of the two transistors together. If the low-power transistor has an hFE of 100 and the high-power transistor has an hFE of 50, together they have an "hFE" of 5,000.

## FETs

The signal gain of an FET is a bit more complicated than with a BJT. The gate current is very small (practically nonexistent with MOSFETs) and the relationship of gate current to drain current is nonlinear. However, the relationship of gate voltage to drain current is fairly linear under certain parameters. For this reason FETs are said to be voltage controlled or that they amplify voltage.

The equivalent of hFE is called transconductance and is defined as follows:

 gm  = ID ————— VGS
Where:

 gm = Transconductance—ratio of drain current to gate voltage ID = Drain current VGS = Voltage between the gate and the source.

However, this relationship isn't as simple as the relationship of base current to collector current in BJTs. First of all, with J-FETs and depletion mode MOSFETs, the relationship is inverse; as gait voltage goes up, drain current goes down. Also, a voltage of several volts may result in a current of several milliamps. You can't compare voltage to current that way (apples to oranges), it appears to be a loss rather than a gain. However, you can design a circuit such that a small change in the gate voltage causes a larger change in the drain-to-source voltage (VDS). This will be covered briefly in Transistor Characteristics.

—————————
 Vocademy