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Appendix A

AFE Equations

This Appendix presents the equations that govern the analog front end, as well as

the AFE bill of materials and a list of gains and breakpoint frequencies. The AFE is

divided into five sub-circuits: Preamplifier, Differential Amplifier, Salen-Key (High

Pass), Salen-Key (Low Pass), and Variable Gain (refer to Figure 3.6). The bill of

materials, including all passive device values, is given in Table A.1

Preamplifier: The preamplifier consists of a passive RC high pass filter and an

active low pass filter with gain. Their transfer functions, respectively, are:

H(s) =s

s + 1R1C1

and

H(s) =s +

1

R2C2+ 1

R3C2

s + 1R2C2

The preamplifier produces a passband gain of 1+ R2R3

= 100, and poles at f= 12R1C1

=

212Hz and f = 12R2C2 = 12.5kHz.

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Device Value Package

R1 110k 0402R2 58k 0402R3 585.8 0402R4 22k 0402R5 39k 0402R6 10.2k 0402R7 39k 0402R8 37.4k 0402R9 90k 0402R10 390k 0402

R11 33k 0402R12 355k 0402R13 390k 0402R14 Maxim 5160 8 pin MAXR15 6.5k 0402C1 6.8nF 0402C2 220pF 0402C3 33nF 0402C4 33nF 0402C5 330pF 0402C6 330pF 0402

Amp 1 Maxim 4253 Dual 10 pin MAXAmp 2 Maxim 4199 8 pin MAXAmp 3 Burr Brown OPA2244 Dual 8 pin MSOPAmp 4 Burr Brown OPA4244 Quad 14 pin TSSOPAmp 5 Analog Devices OP262 Dual 8 pin TSSOP8:1 Mux Analog Devices AD708 16 pin TSSOP16:1 Mux Analog Devices AD706 28 pin TSSOPSPST Switches Maxim 4626 5 pin SOT23-5ADC Analog Devices AD7495 8 pin SOICInput Connector Harwin M80-8681222 2 x 13 array w/ 2mm spacing

Digital Data I/O Advanced Interconnections 30 pin, 50 mil spacingKBA-030-131

Table A.1: AFE Bill of Materials

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Differential Amplifier: The differential amplifier uses an IC with laser trimmed

feedback resistors to achieve a gain of 10. The feedback filter adds a high pass

characteristic. The overall transfer function is:

H(s) =Adiffs

s + 1R4C3

where Adiff = 10 and the high pass filter pole is at f=1

2R4C3= 219Hz.

Salen-Key (High Pass): The equation for the high pass Salen-Key filter is given

by

H(s) = Gs2

s2 + (3G)R5C4

s + 1(R5C4)

2

were G = 1 + R6R7

= 1.26. The high pass pole is at f = 12R5C4 = 123Hz.

Salen-Key (Low Pass): The equation of the first low pass Salen-Key filter is

H(s) =

G

(R8C5)2

s2 +(3G)R8C5 s + 1(R8C5)2

where G = 1 + R9R10

= 1.23. The pole is at f = 12R8C5 = 12.9kHz. The equation for

the second low pass filter is the same as the for the first, substituting R11 for R8, C6

for C5, and with G = 1 +R12R13

= 1.91. The pole is therefore located at f= 14.6kHz.

Variable Gain: The variable gain circuit is governed by the equation:

H(s) = 1 +R14

R15

Note that R14 is a digital potentiometer whose impedance varies from 0 to 200k.

The variable gain therefore ranges from 1 to 32.

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Filter Frequency DampingFirst Order 1.557f Second Order(1) 1.613f 1.775Second Order(2) 1.819f 1.091

Lancaster, 1996 [93]

Table A.2: Standardized Parameters for a fifth order Bessel low pass filter

The low pass circuits combine to form a fifth order Bessel filter. The low pass

portion of the Preamplifier and the second order Salen-Key low pass filters were de-

signed to be consistent with standardized Bessel parameters (Table A.2); the desired

pole location was f = 8kHz. The Preamplifier low pass filter comprises the First

Order portion of Table A.2 : 1.557f = 1.557 8kHz = 12.5kHz. For the Second

Order filters, the Damping parameter was set according to

Damping = 3G

where G is the gain term of the respective low pass Salen-Key filters:

Second Order(1):

pole = 1.613 8kHz = 12.9kHz

G = 3Damping = 1.23

Second Order(2):

pole = 1.819 8kHz = 14.6kHz

G = 3

Damping = 1.91

These are consistent with the low pass filter derivations on pages 114 and 116.

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