# Capacitor Input Filter Calculation

This is a simple means of calculating the required size of the input filter capacitor in a basic power supply, or calculating the peak-to-peak ripple voltage in an existing supply. It works by assuming that the capacitor supplies current to the load approximately 70% of the cycle—the remaining 30% is supplied directly by the rectified voltage and during this period the capacitor is charged as well.

Graphic

Source or native rfflow file

I was surprised how quickly this graphic went together using Rfflow drawing software. I think this is the first time I was able to create realistic looking sine waves—of course, I have lots of experience with Rfflow.

Peak-to-peak ripple voltage

Peak-to peak ripple voltage is a most useful parameter. By knowing this, the minimum head voltage of a voltage regulator may be easily determined. For instance, the LM7812 series regulator requires a minimum of 2.5V across it to function within specifications. That means the valley of the peak-to-peak ripple voltage may not drop below 14.5V.

Math

Learn these basic relationships—I use them at least weekly…

Q = C * V, C = capacitance in farads, Q = charge in coulombs, V = voltage potential

Q = I * T, I = current flow in amps, Q = charge in coulombs, T = time in seconds

F = 1 /T, F = frequency in hZ, T = period in seconds

Therefore,
I * T = C * V, or C = (I * T) /V

The delta “Δ” symbol indicates a change, such as a change in voltage or a change in time

C = I * ΔT / ΔV

In this case, ΔT = 1 /F e.g. the time period of a 50hZ waveform = 1 /50hZ = 0.02seconds

Therefore,
C = I / (ΔV * F)

Now including the 70% factor we get the final relationship:
C = 0.7 * I /(ΔV * F)
C = capacitance in farads, I = current in amps, ΔV = peak-to-peak ripple voltage, F = ripple freq in hZ
Note that ripple frequency in a full-wave rectifier is double line frequency. For half-wave rectification, the ripple frequency is the line frequency.

Solving for ΔV
ΔV = 0.7 * I /(C * F)

The 70% factor

This is an assumption—in cases where the capacitor is oversize, it will be perhaps 80%, but this is close enough for government work and not very critical.

Putting it to work, a practical example

Assume that we want to make a 9V, 500mA power supply using the LM7809 voltage regulator device, 12V transformer, bridge rectifier and filter capacitor. Line frequency is 50hZ. How large should we make the filter capacitor?

From the spec sheet, we learn that the dropout voltage of the LM7805 is 2.5V. Therefore, the valley of the peak-to-peak ripple should be 9V + 2.5V = 11.5V. Assuming that the average rectified DC voltage is 12VDC, the minimum negative peak of the ripple voltage = 12V – 11.5V = 0.5V. The peak-to-peak ripple voltage is double the peak or 1.0V. Plugging it into the formula:

C = 0.7 * I /(ΔV * F) = 0.7 * 0.5A /(1Vp-p * 100hZ) = 0.0035farads or 3500µf

Selecting the capacitor

Since 3500uf is not a standard value, simply scale up to 3900uf. The maximum value is limited by size and pocketbook—it is not unreasonable to go with 4700uf or 10,000uf—ripple voltage will be proportionately reduced. The DC voltage rating is generally selected to be double the applied voltage or 25V in this case. 35, 50 or 63V would also be acceptable voltage ratings. For experimentation, a 15V capacitor would be OK.

In practice

Should you make such a power supply, do not be at all surprised if the DV voltage you measure is much higher than expected. The reasons are numerous. First, you may not be loading the output to 0.5A and/or the transformer may be rated for higher current. In such cases, the capacitor will tend to peak charge to the peak of the AC waveform. The resulting voltage may be 15 or 16V or so. It is important to know this because the LM7909 regulator must now dissipate perhaps double the expected power. In other words, it will require a larger heat sink to run at an acceptable temperature.

For the future

Novel voltage doubler circuits

Undocumented words and idioms (for our ESL friends)

close enough for government work—idiom, there is a right way and a wrong way to accomplish a given task…and then there is the government way…or the army way…

limited by the pocketbook—idiom, limited by available funds

##### Related Tutorials

• Sujit

Dear Sir I am making a supply of 24V where the transformer output is 24V 1.2A. From transformer I am taking two output, one from half wave rectifier to drive CD40106 and another with full wave rectifier to drive 4060 counter. My question is what be the value of input capacitor in my case since I don’t know what will be the voltage dropout in my circuit.

• Jim Keith

I think that you are getting yourself into trouble using both full and half-wave rectifiers off the same transformer. If such is the case, the counter chip cannot be connected to the inverter chip because there will be a high AC voltage component between the two ground rails. For a 1.2A transformer these two loads are flea power. If there is a significant load on the half-wave rectifier, the transformer will tend to saturate thus greatly increasing its magnetizing current and potentially causing it to overheat. The DC output of a lightly loaded 24V transformer is roughly 24 * 1.2 * 1.414 = 40V that is generally too high for most 3-terminal regulators. Regarding the input capacitor, virtually any capacitance will work for flea power (microamp load). Consider using a lower voltage transformer and connecting both chips to the same power supply rails (common & positive rails). Good luck–hope that I haven’t confused you.

• salman

sir have to make power supply of 5v by usig the smoothing capacitor of 2200uf…but i have to find the value 2200uf theoretically first.. how can i find the value…i m also usig the LM7805

• Lexander

Sir, i want to ask how to calculate the capasitor for dc to dc stepdown? Using regulator like 7805. Thank you

• Tayyab

A certain full-wave rectifier has a peak out voltage of 40 V.A 60 F capacitor input filter is connected to the rectifier. Calculate the peak-to-peak ripple and the dc output voltage developed across a 500 Ω load resistance.

plz solve this question

Thanks

Tayyab

• Able Utopia

The entire calculation is unpractical. If you are using a voltage regulator IC, an input capacitor of such gross large value has no purpose. The voltage regulator is supposed to smooth the rectifier’s ripple. Check the spec’s data sheets.

• Jim Keith

Please note that a series voltage regulator can only reduce voltage –it will drop out of regulation when it has no head voltage. On the other hand, if there is good head voltage a much smaller input capacitor may be used –however, the power dissipated by the series regulator will be substantially increased –many trade-off issues to consider…

• Tareq

Dear sir
I want To make 3 Phase power Supply . Load = 2 kW Motor , Supply Voltage 350 v , please Tell me the require capacitor Size ?

• Jim Keith

Good question. In three phase to DC rectifiers, no filter capacitor is required for a pure resistive load because the voltage ripple is inherently low. However, as in your case, the typical load is a variable frequency three phase inverter –PWM or 6-step. In this case, there are reactive load elements that feed pulses of current back into the DC source. Thus a “bus capacitor” is required. Such a capacitor is generally rated by both series resistance and AC current rating –I forget any practical rule of thumb for determining the current rating, but it may be close to the motor phase current.

Another issue is regeneration in which the rotating energy of an the motor is dumped back into the bus capacitor as the motor is rapidly reduced in speed (frequency). This tends to cause the bus capacitor voltage to be pumped up well beyond the normal voltage. In this case, a switched or active resistance dissipator is required to absorb such energy.

Another issue is that of pre-charge current limitation because when the AC power is applied, the capacitor provides a momentary short circuit across the output thus resulting in a very high transient current. This is generally solved by applying power with a pre-charge resistor in series with the capacitor and shorting such resistor with a relay contact when the voltage rises to normal.

Bus capacitors are sometimes film type rather than aluminum electrolytic. To obtain adequate voltage rating (e.g. 700VDC for 460VAC mains), aluminum capacitors must be connected in series. Film capacitors are available with a higher voltage ratings, and due to their extremely low ESR (effective series resistance) the current rating is increased over that of aluminum. As a result, film capacitors are lower in capacitance.

While this does not fully answer your question, it provides food for thought and should help steer you in the correct direction.

• sandeep

you have explained so simply there is no ripple in mind.

• bhavesh

From the spec sheet, we learn that the dropout voltage of the LM7805 is 2.5V. Therefore, the valley of the peak-to-peak ripple should be 9V + 2.5V = 11.5V. Assuming that the average rectified DC voltage is 12VDC, the minimum negative peak of the ripple voltage = 12V – 11.5V = 0.5V.

could you plz expain this with figure??

• Jim Keith

In this case, the ripple voltage component is 0.5V peak, or 1V peak to peak. This provides the delta V that we can plug into the capacitor calculation formula. Confusing, but simple at the same time.

• khan

Thank u sir for anser

1Vp-p is the AC peak to peak ripple voltage that appears across the capacitor. This adds and subtracts from the DC voltage level.

Can u tell me how to find outripple factor With formula

• khan

Sir can u explain me
C=0.7*0.5A/(1Vp-p*100hz)
What is 1Vp-p?
What is 0.7?
I hope u sir u clear my dought

• Jim Keith

1Vp-p is the AC peak to peak ripple voltage that appears across the capacitor. This adds and subtracts from the DC voltage level.

The factor “0.7” is the assumption that the capacitor supplies the load for 70% of each half-cycle, and the rectifier output supplies the load for the remaining 30% while charging the capacitor at the same time.

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