# Math formulas

### Useful for linear PSU and audio

Most of these calculation will prove less accurate when simulated or protyped on the work bench.

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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