MFB Single Amplifier Biquads

MFB (also known as Bridged T and Negative Gain SAB) single amplifier biquads (SAB's) are negative gain for all but notch stages implemented with an injector resistor. The inclusion of injector resistor, R8, reverses the sign of the gain, making the gain of the MFB SA positive. This network can realize any filter (low pass, high pass, band pass, band stop, high notch, low notch, and all pass) with positive element values. The inclusion of injector resistor R8 reverses the sign of the gain.

 

The Main Advantage of negative SA's to positive SA's are:

  1. Generally lower element error sensitivity and sometimes a lower element count.

  2. A lower element count is sometimes needed.

 

The Main Disadvantage of negative SA's to positive SA's are:

  1. Generally higher opamp error sensitivity, although this error may be minimized for high Q stages with the use of positive feedback enhancement (Resistors R9 and R10).

  2. Fixed gain selection for notch stages.

 

The element count and sensitivities to element value and opamp error vary from configuration to configuration and should be checked prior accepting a stage topology.

The generic low pass form for the negative SA is shown below.

 

Not all of the resistors and capacitors are needed at the same time. The table below states the functions of the individual elements.

Element

Function

R1, C2

These elements are used to create third order filters. High pass filters interchange the resistor and capacitor. If a second order stage is specified, these elements are not installed. Third order stages are not available for all pass stages.

 

C3, R4, R5, C6

These elements comprise the basic MFB filter. They are ALWAYS installed for second and third order filters. C3 and R4 are present in first order filters. Resistors and capacitors are interchangeable depending on the type of filter being designed (high pass, band pass, etc.).

 

R7

This element is used to control gains for second and third order filters. It is usually, but not always, installed. It may also be a capacitor.

 

R9, R10

These are the positive feedback enhancement resistors. Their presence is optional and they have the effect of reducing opamp sensitivity to high Q (Q>=10) filters. These elements are always resistors.

 

R8

This element is known as the injection resistor. Its presence converts the gain from negative to positive. It is installed on band stop, notch, and all pass filters. The presence of this resistor also fixes the gain of the filter in second order stages.