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### Multistage active filters: The Reactive Voltage Divider Approach

Another method to create active filters using opamps is to create a voltage divider with a resistance and a reactance (from a capacitor). This approach has some advantages over the previously mentioned filters: they are easy to build, easy to understand, and have "programmable" gain.

In the reactive voltage divider, the input is applied to the non inverting input of the opamp. This is so that it can be used as a simple non inverting amplifier, the gain being set by extra resistors that do not interfere or need to be considered much in the filter's working; they are just there to set the amplifier feedback's gain.

The signal is applied in series with one of the components and taken at the input in parallel with the second. The choice of which component is in series and which in paralel with the non inverting input has direct consequences in the functioning of the filter.

If the series component is chosen to be a resistor, then the voltage at the capacitor will determine the signal to be amplified. Since the reactance of the capacitor gets lower with frequency, the higher the frequency the lower the signal available at the opamp input (remember the voltage divider formula: (Vin*R2)/(R1 + R2), in this case, it becomes (Vin*Xc)/(Xc + R) where Xc is the capacitive reactance); This configuration gives us a low pass filter.

With the capacitor being the series component, the voltage at the resistor now determines the signal available at the opamp input. As the frequency gets higher, the capacitor's reactance lowers, up to the point where it acts almost as just a wire; this means that the higher the frequency the more signal available to the opamp. This configuration gives us a high pass filter.

These two main types of voltage divider filters can be cascaded (The output of the first used the the input of the second) in a single stage (one opamp, multiple voltage dividers) or multiple stages (one opamp per voltage divider), the latter having better characteristics due to the opamp's compensating mechanisms.

## Welcome To Electronic Circuits For Beginners!

All circuits included here are recommended to be assembled in printed circuit boards. Printed circuit boards, or PCB's increase the circuit reliability and mechanical stability.

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Led chaser circuit

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Simple power supply

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All circuits include parts list and complete How-it-works for beginners and hobbyists to easily understand.