Math formulas

Easy to use online Ohm's Law Calculator

Easy to use online E series of preferred numbers

Calculate output noise from LDO with gain

Output noise is typically proportional to the gain so we calculate from unity-gain configuration. From datasheet find these parameters:

• Unity-gain RMS noise: 40μV
• Unity-gain output voltage: 1.2V
• Desired output voltage: 5.1V

Gain Factor = (5.1V / 1.2V) = 4.25
Noise at new gain = 40μV×(sqrt((5.1V / 1.2V))) ≈ 82.4 μV
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Calculate the reservoir capacitance

        C=I*t / ΔV     where:

• C - is the capacitance in farads
• I - is the DC load current in amperes
• t - is the period of the full-wave rectified waveform, in seconds 50Hz t=0.01, 60Hz t≈0.0167
• ΔV - is the allowable ripple across the load, in volts

3 amp load, 50Hz mains and 0.5 volt of ripple then
C = 3A*0.01s / 0.5V = 60,000µF
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It might be more useful to input required current and capacitor value and see what ripple voltage comes out from this.
V_PSRR = 3I * 0.01t / (33000μF / 1000000))
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Calculate the ripple suppression in LDO

        Vout = VRin / (10^(PSRR/20))

• VRin is ripple voltage factor
• PSRR is typical given in dB at 120Hz

If datasheet say 53dB and ripple voltage is 0.1V then
Ripple Voltage = 0.1 / (10 ^ (53 / 20)) ≈ 0.000224V
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We can change this formula to also include the reservoir cap
µVT_PSRR = (((0.5I * 0.01t) / (20000μF / 1000000)) / (10^(53dB/20))) * 1000000 ≈ 600µV
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Calculate transformer secondary voltage from nominal voltage

These examples uses 6.3V nominal voltage.

Vdc = (2*6.3)/3.14159265359 = 4.01 V
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Vrms = 6.3*(sqrt(2)) ≈ 8.91 V
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Ripple faktor = Vr = Vpeak/Vdc = 6.3 / 4 = 1.575 V
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Transformer Series Resistance

Re = Rp / (Tr)² where

• Re is equivalent primary resistance
• Rp is measured primary resistance = 15Ω
• Tr is the turns ratio = 240V / 5V = 48

15 / ((240/5) ^ 2) = 0.0065Ω
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Total series resistance of the transformer = Secondary resistance + above calculation Source: https://sound-au.com/power-supplies.htm

Convert voltage to dBV

dBV = 20*log((1Vref*1000000000)/12.78nV) ≈ 157.9dBV
One can change the value of Vref to PSU output voltage to get dB with reference to actual implementation. This is not the same as dBV though.
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Simplified voltage to dBV could look like this where all numbers are in V.
20*log(1/0.00000001278) ≈ 157.9dBV
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