Active Low Pass Filter

Active Low Pass Filters

In the RC Passive Filter tutorials, we saw how basic 1st-Order filter circuits, such as the Low Pass and the High Pass filters can be made using just a single resistor and a non-polarized capacitor connected in series across a sinusoidal input signal. We also noticed that the main disadvantage of passive filters is that the amplitude of the output signal is less than that of the input signal, ie, the gain is never greater than 1. With filter circuits containing multiple order stages, this loss in amplitude called "Attenuation" can become quiet severe. One way of restoring or controlling this loss of signal is by amplification through the use of Active Filters.

As their name implies, Active Filters contain active components such as operational amplifiers or transistors within their design. They draw their power from an external power source and use it to boost or amplify the output signal. Operational amplifiers can also be used to shape or alter the frequency response of the circuit by producing a more selective output response by making the output bandwidth of the filter more narrower or even wider.

Active filters generally use Operational Amplifiers within their design and in the Operational Amplifier tutorial we saw that an Op-amp has a High Input impedance, a Low Output impedance and a Voltage Gain resulting from the resistor combination within its feedback loop. Unlike a passive High pass RC filter that has infinite high frequency response, the maximum frequency response of an active filter is limited to the Gain/Bandwidth product (or open loop gain) of the operational amplifier being used. Still, active filters are generally more easier to design than passive filters, they produce good performance characteristics, very good accuracy with a steep roll-off and low noise when used with careful circuit design.

Active Low Pass Filter

The most common and easily understood active filter is the Active Low Pass Filter. Its principle of operation and frequency response is exactly the same as that for the previously seen RC low pass filter, the only difference being it uses an op-amp for amplification and gain control. The simplest form of a low pass active filter is to connect an inverting or non-inverting amplifier, the same as those discussed in the Op-amp tutorial, to the basic RC low pass filter as shown.

First-order Low Pass Butterworth Filter

This 1st-Order low pass Butterworth type filter, consists simply of a passive RC filter connected to the input of a non-inverting operational amplifier. The frequency response of the circuit will be the same as that of the passive RC filter, except that the amplitude of the output signal is increased by the passband voltage gain of the amplifier and for a non-inverting amplifier this given as: 1 + R2/R1.

For a non-inverting amplifier circuit, the magnitude of the voltage gain for the filter is given as a function of the feedback resistor (R2) divided by its corresponding input resistor (R1) value and is given as:

Voltage Gain for a First-order Low Pass Filter

• Where:
•   A_F = the Passband Gain of the filter, (1 + R2/R1)
•   ƒ = the Frequency of the Input Signal in Hertz, (Hz)
•   ƒc = the Cut-off Frequency in Hertz, (Hz)

When dealing with filter circuits the magnitude of the pass band gain of the circuit is generally expressedin Decibels or dB as a function of the voltage gain, and this is given as:

Magnitude of Voltage Gain in (dB)

Example No1.

Design a Non-inverting Low Pass filter circuit that has a gain of 10 at low frequencies, a high frequency cut-off point or corner frequency of 159Hz and an input impedance of 10KΩ.

The voltage gain of a Non-inverting operational amplifier is given as:

Assume a value for resistor R1 of 1kΩ rearranging the formula gives a value for R2 as  

then, for a voltage gain of 10, R1 = 1kΩ and R2 = 9kΩ.

converting this voltage gain to a decibel dB value gives: 

The cut-off or corner frequency (ƒc) is given as being 159Hz with an input impedance of 10kΩ. This cut-off frequency can be found by using the formula:

where ƒc = 159Hz and R = 10kΩ.

then, by rearranging the above formula we can find the value for capacitor C as:

Then the final circuit along with its frequency response is given below as:

Low Pass Filter Circuit.

Frequency Response Curve

If the external impedance connected to the input of the circuit changes, this change will also affect the corner frequency of the filter (components connected in series or parallel). One way of avoiding this is to place the capacitor in parallel with the feedback resistor R2. The value of the capacitor will change slightly from being 100nF to 110nF to take account of the 9kΩ resistor and the formula used to calculate the cut-off corner frequency is the same as that used for the RC passive low pass filter.

An example of the new Active Low Pass Filter circuit is given as.

Simplified Non-inverting Amplifier Circuit

Equivalent Inverting Amplifier Circuit

Applications of Active Low Pass Filters are in audio amplifiers, equalizers or speaker systems to direct the lower frequency bass signals to the larger bass speakers or to reduce any high frequency noise or "hiss" type distortion. When used like this in audio applications the active low pass filter is sometimes called a "Bass Boost" filter.