8.2.1 Design Requirements

As a design example:

Require: A_LP = 10, less than 1dB passband ripple, and a cutoff frequency of 1kHz.

8.2.2 Detailed Design Procedure

There are many resources discussing the Sallen-Key lowpass filter topology.

Texas Instruments has made filter design easy by creating on-line and stand alone design tools, such as Webench Filter Designer and Filter Pro Desktop.

For this design, the stand-alone Filter Pro Desktop is used.

For the design, the following parameters are entered into the Filterpro software:

• Filter Type = Lowpass
• Gain = 10 V/V (20dB)
• Passband Frequency = 1 kHz
• Allowable Ripple = 1 dB
• Filter Order = Checked and set to 2
• Response Type = Butterworth
• Filter Topology = Sallen-Key
• Component Tolerance - Resistor = E96 1%
• Component Tolerance - Capacitor = E6 20%

After entering these values, FilterPro returns the following recommended values:

• R1 = 44.2 kΩ
• R2 = 38.3 kΩ
• R3 = 2.49 kΩ
• R4 = 22.6 kΩ
• C1 = 10 nF
• C2 = 1.5 nF

The LMV551-Q1 is targeted for low power operation. The above resistor values are assumed for a standard power application. To save both quiescent and dynamic power, increase the value of the resistors.

The largest consumer of power is the gain setting feedback resistors R3 and R4, as these are DC coupled and represent a constant DC load to the amplifier. If the output is biased at 2.5 V, then 2.5 V / (22.6 kΩ + 2.49 kΩ) = 99.6 µA is flowing through the feedback network. This is significantly more than the 37uA quiescent current of the amplifier alone! Increasing the size of the feedback resistors by a decade from 22.6kΩ to 226kΩ, the current in the feedback network can be reduced down to 9.9µA.

Increasing the resistor values requires a proportional decrease in the values of the capacitors. If a resistor value is increased 10×, then the corresponding capacitor value must be decreased 10×. However, note that increasing the resistor values increases the contributed noise, and decreasing the capacitors to small values increases the sensitivity to stray capacitance.

There is a decision to be made about also scaling the filter components (R1, R2, C1 & C2). R1 and R2 are AC coupled to the output, so the only DC current flowing through these resistors is the input bias current of the LMV551-Q1 (typically 20 nA). However, large AC currents can flow through C2 and C1 during large signal swings. Scaling the filter components also reduces the peak AC signal currents. If the AC signals are expected to large (several Vpp) and frequent, then scaling the filter values may be beneficial to overall power consumption. If the expected AC signals are small, it may not be worth the noise tradeoff to scale these values.

Because the LMV551-Q1 has a bipolar input, to maintain DC accuracy, the equivalent resistance seen by each amplifier input should be equal to cancel the bias current effects.

To maintain DC accuracy through bias current cancelling, the following relationship should be maintained:

Fortunately, the filter Pro software makes changing and recalculating the values easy. By changing the value of any of the filter components (R1, R2, C1 & C2) in the schematic tab, the program automatically recalculates and scale these components. Conversely, changing the gain feedback components (R3 or R4) also causes the other feedback resistor to scale. However, Filter Pro does NOT maintain the relationship between the feedback and filter elements as described in Equation 4 above. The feedback resistor values can be 'seeded' and scaled appropriately, as long as the original feedback resistor ratio is maintained.

Figure 30. 1-kHz Sallen-Key Low Pass Filter with Values

8.2.3 Application Curve

Figure 31 shows the simulated results of the example 1-KHz Sallen-Key Low Pass Filter.

Figure 31. 1KHz, 2-Pole Sallen-Key Low Pass Filter Results