# A Primer on the Design of Active Filters - Part II

### Filter Topologies - Implementing Approximation Stages as Real Circuits

Having chosen an Approximation, with one or more stages, it is now time to realize each stage as an actual circuit.

**Each topology (circuit) has a range of characteristics that you may want to considered, including:**

- actual (versus optimal) gain realized
- number of components required, including op amps
- spread in component (RC) values
- ease of tuning (if applicable)
- input impedance as a function of frequency
- op amp Gain Bandwidth required
- relative noise
- gain-frequency variability to be expected due to tolerances and temperature change

### For example, shown below are some choices available for implementing a 2nd order Band Pass stage, each with its own advantages and disadvantages:

Deliyannis I | Deliyannis II |

Sallen-Key | Multiple Feedback I |

Multiple Feedback II | Fliege |

Twin-T | KHN |

KHN Inverting | Tow-Thomas |

MB | Berka-Herpy |

Akerberg-Mossberg | PMG |

Natarajan | |

### Why choose 3 or 4 op amp topologies when there are 1 or 2 op amp alternatives?

One may do so for any of the following reasons:

- ease of tuning
- lower sensitivities to passive components and parasitics
- more versatile - perhaps can implement LP, HP and BP
- realize higher Q values
- realize higher gain
- sometimes they are the only topologies that will implement a notch stage

### Active filter software can make design choices easier:

Passive Sensitivities ChartThe frequency response of any filter stage can be completely specified by a gain constant (To), the Quality Factor (Q), the pole frequency (fp), and in the case of notches, the zero frequency (fz). This chart illustrates the sensitivity of these parameter to slight changes in the stage resistor and capacitor values. |
Gain Spread ChartGain spread is a relative measure of the random variability in stage gain likely to be contributed by each resistor and capacitor, in accordance with the currently specified resistor and capacitor tolerances. |

Op Amp Dynamic Range ChartThis chart indicates what percentage of the available voltage output range, of each filter stage, is being utilized. An ideal filter would have 100% dynamic range for each filter. |
Stage Gain ChartThe gain of the stage is simulated using an op amp model with single-pole roll off, and can be compared with the ideal gain-frequency response. A mismatch of the two curves generally indicates the specified op amp Gain Bandwidth is too low. |

Input Impedance ChartThe stage input impedance is charted as a function of frequency. A higher input impedance will present less loading of the signal source in advance of the filter stage. |
Monte Carlo ChartThe chart presents a simulation of variability in stage gain versus frequency that could be anticipated due to tolerances in resistor and capacitor values, as well as in op amp Gain Bandwidth (the latter is never specified in datasheets, and can vary considerably). |

### Scaling Component Values

In general, one would choose 1% E-96 resistors and 1-5% E-12 or E-24 capacitors. The design software should be capable of scaling component values - by increasing all capacitor values and decreasing the appropriate resistor values, or by decreasing all capacitor values and increasing the appropriate resistor values.

**The reasons for scaling components may be:**

- low power applications dictating high resistor values (and more noise)
- high frequency applications requiring smaller resistor values (and more power)
- stage input impedance needing to be modified
- only particular component values being readily available