Filters

All of these filters have adjustable cutoff frequencies using a digital potentiometer, expect for the 60 Hz notch filter. For a recap on how the basic building blocks for the architecture I used works, see the parent page:

60 Hz Notch Filter

Filter Layout

Transfer Function

SPICE Simulations

Non Logarithmic Scale

Logarithmic Scale

6th Order High/Low Pass

Because the transfer functions are very similar for both the low pass and high pass filters, the same circuit can be used for both. The only difference being where the filter is cascaded from. By using analog multiplexers, the points at which the circuits are cascaded from can change very easy. This saves the amount of components that need to be used for the design.

The idealized version of a 6th order Butterworth filter for both high pass and low pass can be shown below. By varying RQ, the desired frequency responses can be achieved. The following equations are the transfer functions for both the 6th Order Low Pass and 6th Order High Pass filters.

High Pass Version

Low Pass Version

As seen in both the two circuit drawings above, the only major difference between the two filters is where they are cascaded from. The ratios of RQ and R are the same for both filters, so a single circuit with analog multiplexers can accomplish both the high pass and low pass versions.

Due to the availability of certain values of resistors, the idealized values were not used. Instead, the desired values were found by adjusting how much resonance there is for different parts of the fiters. This was done by trial and error until a nearly ideal response was found using the resistor values readily available on Digikey, Mouser and Newark. The separate responses for the filters with their resonance can be seen in below.

SPICE Simulations

Filter Resonances

6th Order Low Pass (Logarithmic Scale)

6th Order High Pass (Logarithmic Scale)

6th Order Bandpass

The 6th Order Bandpass Filter is created by cascading a highpass version the basic filter on the parent page, a low pass version that same filter, a first low pass and a first order high pass. The equations for the idealized version of the 6th Order Bandpass Filter can be seen below. The very last output buffer is shared with all of the filters as well through the analog multiplexer. This saves the number of chips used to implement the CyDAQ, greatly reducing the cost.

Filter Layout

SPICE

(Logarithmic Scale)

1st Order High Pass

The 1st Order HIgh Pass Filter also shares the output buffer with both the 1st Order Low Pass and 2nd Order Bandpass. The node going into the positive terminal on the operational amplifier comes out of an analog demultiplexer after going into the multiplexer from the node shared by C1 and RF1.

Filter Layout

SPICE Simulation

(Logarithmic Scale)

1st Order Low Pass Filter

This filter has a buffer, but the output unity gain buffer is shared between the 1st Order Low Pass, 1st Order High Pass, and the 2nd Order Band Pass. The actual buffer comes after the analog demultiplexer on the CyDAQ 2.0 test board. This helps cut down on the number of amplifiers needed to make the board.

Filter Layout

SPICE Simulation

(Logarithmic Scale)

2nd Order Bandpass Filter

The filter below has both an upper and lower corner that are programmable with the digital potentiometers shown in Table 3. The output buffer is shared with the 1st Order Low Pass and the 1st Order High Pass Filter.

Filter Layout

SPICE Simulation

(Non Logarithmic Scale)