SME
Electronics · Problem type
Current gain: IC, IE and α from β
Use this for “A BJT with β = 100 has a base current of 20 μA. Find IC, IE and α.”
This is an example. Type your own values to start a new problem.
IC (mA)
=
β
×
IB (μA)
IE (mA)
=
(
β
+
1)
×
IB (μA)
α
=
β
+
1
Formulas
IC
=
β
×
IB
2 = 100 × 0.02
IE
=
(
β
+
1)
×
IB
2.02 = (100 + 1) × 0.02
α
=
β
β
+ 1
0.9901
=
100
100 + 1
Formulas are worked in mA. The step-by-step shows the conversions.
Assumptions
•
The transistor is in active mode, where the collector current is β times the base current.
•
The emitter carries both currents: IE = IB + IC = (β + 1)IB.
•
α = IC ÷ IE, the share of the emitter current that reaches the collector.
Step-by-step
WE KNOW
β = 100, IB = 20 μA
FIND
collector current (IC), emitter current (IE), common-base gain (α)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to mA).
IB = 20 μA = 0.02 mA (1 mA = 1000 μA)
Step 2 · Find collector current (IC)
Use IC = β × IB
In
active
mode
the
collector
carries
β
times
the
base
current.
IC = 100 × 0.02
IC = 2 mA
Step 3 · Find emitter current (IE)
Use IE = (β + 1) × IB
The
emitter
carries
the
base
current
and
β
times
it
again.
IE = (100 + 1) × 0.02
IE = 101 × 0.02
IE = 2.02 mA
Step 4 · Find common-base gain (α)
Use α = β ÷ (β + 1)
IC
IE
=
βIB
β
+ 1
IB:
the
base
current
cancels.
α
=
100
100 + 1
α
=
100
101
α
=
0.9901
Check
Put the numbers back in. Both sides should match.
2 = 100 × 0.02 ✓
2.02 = (100 + 1) × 0.02 ✓
0.9901
=
100
100 + 1
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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