Aktif Alçak Geçiren Filtre / Active Low Pass Filter

In RC passive filter tutorials, we have seen how basic premium filter circuits, such as low-pass and high pass filters, can be serially made using only a single resistance with a non-polarized capacitor connected to 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 the input signal, that is, the gain is never greater than the union, and the load impedance affects the properties of the filters.

With passive filter circuits containing multiple stages, this loss of signal amplitude, called "weakening", can become silent. One way to recover or control this signal loss is the use of amplification through the use of active filters.

As the name suggests, active Filters contain active components such as operational amplifiers, transistors or FET's in circuit designs. They draw their power from an external power source and use it to increase or amplify the output signal.

Filter amplification can also be used to shape or change the frequency response of the filter circuit by generating a more selective output response. This makes the filter's output bandwidth narrower or wider. In short, the main difference between "passive filter" and "active filter" is amplification.

An active filter usually uses an operational amplifier (op-amp) in its design, and in the operational amplifier tutorial we found that an Op-amp has a high input impedance, a low output impedance, and a voltage gain determined by the resistance network.

Unlike a passive high-pass filter, which theoretically has an 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 used. However, the design of active filters is often much easier than passive filters, when used with a good circuit design they produce very good accuracy with good performance characteristics, a steep rolling and low noise.

Active Low Pass Filter

The most common and easy-to-understand active filter is the active low-pass filter. The operating principle and frequency response are exactly the same as the passive filter seen before, this time the only difference is that it uses an op-amp for amplification and gain control. The simplest form of a low-pass active filter is to connect an untranslated or inverted untranslated amplifier to the basic RC low-pass filter circuit, as shown, which is the same as those discussed in the Op-amp tutorial.

First Degree Low Pass Filter

Active Low Pass Filter
First Degree Low Pass Filter

The primary low-pass active filter consists of a passive RC filter stage that provides a low frequency path to the input of an inverted operational amplifier. Unlike the previous passive RC filter, which had less DC gain than the union, the amplifier is configured as a DC gain, Av = +1, or a voltage tracker (buffer) that yields unity gain.

The advantage of this configuration is that the high input impedance of op-amps prevents overloading the output of filters, while the low output impedance prevents the filters from being affected by changes in the load impedance of the cutting frequency point.

While this configuration provides good stability to the filter, its main drawback is that there is no voltage gain on one. However, although the voltage gain is uneasy, the power gain is very high, as the output impedance is much lower than the input impedance. If more than one voltage gain is required, we can use the following filter circuit.

Active Low Pass Filter with Amplification

Active Low Pass Filter
Active Low Pass Filter with Amplification

The frequency response of the circuit will be the same as the passive RC filter. However, the amplitude of the output is increased by the amplifier's AF transition band gain. In an inverted amplifier circuit, the size of the voltage gain for the filter is given as a function of the feedback resistance (R2), which is divided by the corresponding input resistance (R1).

Active Low Pass Filter
Gain

Therefore, the gain of an active low-passing filter as a function of the frequency:

Gain of First-Degree Low Pass Filter

Active Low Pass Filter
Gain of First-Degree Low Pass Filter

AF = transition band gain of the filter, (1 + R2 / R1)
ε = frequency of the input signal in Hertz,
(Hz) εc = Cutting frequency in Hertz, (Hz)
Therefore, the operation of a low-pass active filter can be verified from the equation of frequency gain above:

At very low frequencies, ε < ƒc

Active Low Pass Filter

Cut-off frequency,in F = εc

Active Low Pass Filter

At very high frequencies, ε > εc

Active Low Pass Filter

Therefore, the active low-pass filter has a frequency breakpoint higher than 0 hz, a fixed gain AF to εc. Earnings in ΕC are 0.707 AF and decrease at a constant rate as frequency increases after εc. That is, when the frequency increases tenfold (decade), the voltage gain is divided by 10.

In other words, earnings are reduced by 20db (= 20*log(10)) every time the frequency is increased by 10. When dealing with filter circuits, the size of the transitional band gain of the circuit is usually expressed as decibels or dB as a function of voltage gain, and this is defined as follows:

The size of the voltage gain (dB)

Active Low Pass Filter
The size of the voltage gain (dB)

Active Low Pass Filter Example

Let's learn together how to design an inverted active low pass filter circuit with ten gain, high frequency cutting or 159hz corner frequency and 10kω input impedance at low frequencies.

The voltage gain of an undemode operational amplifier is given as follows:

Active Low Pass Filter

1kω resistance gives A value for R2 to rearrange the above formula, suppose a value for R1:

Active Low Pass Filter

Converting this voltage gain to an equivalent decibel dB value is done as follows.

Active Low Pass Filter

The cutting or corner frequency (εc) is given as 159Hz with 10kΩ input impedance. This cutting frequency can be found using the following formula:

Active Low Pass Filter

By rearranging the above standard formula, we can find the value of filter capacitor C as follows:

Active Low Pass Filter

Therefore, the last low-pass filter circuit, together with the Frequency response, is given below:

Low Pass Filter Circuit

Active Low Pass Filter

Frequency Response Curve

Active Low Pass Filter

If the external impedance connected to the input of the filter circuit changes, this impedance change also affects the corner frequency of the filter (components connected to each other in series or parallel). One way to avoid any external influence is to place the capacitor in parallel with the feedback resistance of R2, effectively removing it from the inlet, but in this case still retaining the properties of the filters.

Union Non-Gain Reverse Amplifier Filter Circuit

Active Low Pass Filter
Union Non-Gain Reverse Amplifier Filter Circuit

Here, due to the position of the capacitor parallel to the R2 feedback resistance, the low transition angle frequency is adjusted as before. However, at high frequencies, the recess of the capacitor reduces the gain of amplifiers, causing R2 to short-circuit. At a sufficiently high frequency, as the amplifier effectively becomes a voltage tracker, the gain dips to the bottom in the union (0dB), so that the gain equation is 1 + 0/R1, which equates to 1 (union).

Grade II Low Pass Active Filter

As with a passive filter, a first-degree low-pass active filter can be converted from a second-degree low-pass filter using an additional RC network on the input path. The Frequency response of the filter that is lower than the second order is the same as that of the type of first order, except that the rounding of the stop tape is twice that of the first level filters of 40dB/decade (12dB/octave). Therefore, the necessary design steps of the second-degree active low-pass filter are the same.

Grade II-Listed Active Low-Pass Filter Circuit

Active Low Pass Filter
Grade II-Listed Active Low-Pass Filter Circuit

When combining filter circuits to create higher-order filters, the total gain of the filter is equal to the product of each stage. For example, the gain of one stage can be 10, and the gain of the second stage can be 32, and the gain of the third stage can be 100. The total earnings will then be 32,000 (10 x 32 x 100), as shown below.

Cascading Voltage Gain

Active Low Pass Filter
Cascading Voltage Gain
Active Low Pass Filter

Active filters from the second order (bipolar) are important because higher-order filters can be designed using them. By combining first- and second-degree filters, filters with any single or double value can be created.