SME
Electronics · Problem type
Bridge rectifier with a filter capacitor
Use this for “A bridge rectifier on a 12 V peak secondary feeds 470 μF and 1 kΩ. Find the ripple and the dc output.”
Diagram
Vₚ = Vsec − 2·VD
Vₚ = 12 V − 2 × 0.7 V = 10.6 V
Vᵣ
=
Vₚ
fᵣ·RC
Vᵣ
=
10.6
V
120 Hz × 1 kΩ × 470 μF
Vᵣ = 0.1879 V
Vdc
=
Vₚ
−
Vᵣ
2
Vdc
=
10.6
V
−
0.1879
V
2
=
10.51
V
Two diodes conduct each half cycle, so the ripple comes at twice the line frequency.
Dashed: the wave without C; solid: C’s voltage, drawn to scale.
This is an example. Type your own values to start a new problem.
Vₚ (V)
=
Vsec (V)
−
2
×
VD (V)
Vᵣ (V)
=
Vₚ (V)
fᵣ (Hz)
×
R (kΩ)
×
C (μF)
Vdc (V)
=
Vₚ (V)
−
Vᵣ (V)
2
Formulas
Vₚ = Vsec − 2 × VD
10.6 = 12 − 2 × 0.7
Vᵣ
=
Vₚ
fᵣ ×
R
×
C
0.1879
=
10.6
120 × 1,000 × 0.00047
Vdc
=
Vₚ
−
Vᵣ
2
10.506
=
10.6
−
0.1879
2
Vdc
=
Vₚ
×
(1
−
1
2 × fᵣ ×
R
×
C
)
10.506
=
10.6
×
(1
−
1
2 × 120 × 1,000 × 0.00047
)
Formulas are worked in Ω, F. The step-by-step shows the conversions.
Assumptions
•
Two diodes conduct each half cycle, so the peak loses 2VD; the ripple is at twice the line frequency.
•
Between peaks C discharges through R in a near-straight line (the ripple is well under Vₚ).
•
R in Ω and C in F, so fᵣ RC has no unit.
Step-by-step
WE KNOW
Vsec = 12 V, VD = 0.7 V, fᵣ = 120 Hz, R = 1 kΩ, C = 470 μF
FIND
output peak (Vₚ), ripple (peak to peak) (Vᵣ), dc output (Vdc)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to Ω, F).
R = 1 kΩ = 1,000 Ω (1 kΩ = 1000 Ω)
C = 470 μF = 0.00047 F (1 F = 10⁶ μF)
Step 2 · Find output peak (Vₚ)
Use Vₚ = Vsec − 2 × VD
Two diodes in the path, each taking its drop off the peak.
Vₚ = 12 − 2 × 0.7
Vₚ = 12 − 1.4
Vₚ = 10.6 V
Step 3 · Find ripple (peak to peak): Vᵣ
Use Vᵣ = Vₚ ÷ (fᵣ × R × C)
C
loses
about
Vₚ
RC
volts
a
second
for
one
ripple
period,
1
fᵣ
.
Vᵣ
=
10.6
120 × 1,000 × 0.00047
Vᵣ
=
10.6
120,000 × 0.00047
Vᵣ
=
10.6
56.4
Vᵣ = 0.1879 V
Step 4 · Find dc output (Vdc)
Use Vdc = Vₚ − Vᵣ ÷ 2
The output sags from Vₚ by the ripple; its average sits halfway down.
Vdc
=
10.6
−
0.1879
2
Vdc = 10.6 − 0.09395
Vdc = 10.506 V
Check
Put the numbers back in. Both sides should match.
10.6 = 12 − 2 × 0.7 ✓
0.1879
=
10.6
120 × 1,000 × 0.00047
✓
10.506
=
10.6
−
0.1879
2
✓
10.506
=
10.6
×
(1
−
1
2 × 120 × 1,000 × 0.00047
)
✓
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