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Analysis and Application of Analog Electronic Circuits to Biomedical Instrumentation - Northrop.pdf
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Examples of Special Analog Circuits and Systems

533

VB, Gto, and Vs do not change in time, so this steady-state analysis is valid. Using superposition, the system’s response to a time varying, δGt, can be examined. The transfer function, δV2 δGt, can be written:

δV2

(s) =

 

VsKAKP {RC[1+ (ωRFCF )2 ]}

(12.129)

δGt

s(s2

ωn2 + s2ζ ωn + 1+ Vs βKAKP (10RC))

The damping of the cubic closed-loop system is adjusted with the attenuation β. The dc steady-state incremental gain is:

δV2

=

10

 

 

volts siemen

(12.130)

δGt

(1+ (ωRFCF )2

˘

β

 

 

 

˙

 

 

 

 

 

 

˚

 

 

 

A prototype of this system was run at 75 kHz and tested on the chests of

several volunteers after informed consent was obtained. Both δV2 δGt and

·

V1 δGt were recorded. System outputs followed the subjects’ respiratory volumes, as expected.

A second type of IP makes use of a novel self-balancing, two-phase, lockin amplifier (LIA) developed by McDonald and Northrop (1993); the system is described in Northrop (2002). A lock-in amplifier is basically nothing more than a synchronous or phase-controlled full-wave rectifier followed by a low-pass filter. Its input is generally a noisy amplitude-modulated or double- sideband-suppressed carrier ac signal. The LIA output is a dc voltage proportional to the peak height of the input signal; the low-pass filter averages out the noise and any other zero-mean output component of the rectifier. Signal buried in as much as 60 dB of noise can be recovered by an appropriately set-up LIA.

Figure 12.51 illustrates how the LIA is connected to the voltage across the tissue, Vo, where Vo = Is (Rt + jBt), (Bt = 1/ωCt). Note that if the angle of Is is taken as zero (reference), then the angle of Vo is θs = tan1(Bt Rt). The ac reference voltage, Vr, in phase with Is is used to control the LIA’s synchronous rectifier. Vr also allows one to monitor Is because Vr = Is RF. The self-nulling quadrature LIA outputs a dc voltage, Vϕ, proportional to the phase difference between Is and Vo and a dc voltage, Vp, proportional to the magnitude of the impedance, Zt , of the tissue under study. Vp and Vϕ follow the slow physiological variations in Zt caused by blood flow and/or breathing. The modulation of Rt and Bt by pulsatile blood flow or lung inflation can have diagnostic significance.

12.8.5Respiratory Acoustic Impedance Measurement System

Acoustic impedance in this section is defined as the vector (phasor) ratio of pressure (e.g., dynes/cm2) to the volume flow (e.g., cm3 sec) caused by that

© 2004 by CRC Press LLC

534

Analysis and Application of Analog Electronic Circuits

Body part

RF

 

 

 

 

R

Rt

Ct

Is

R

Is

Zt = Rt + 1/jωCt

+ Vo

DA

 

 

 

 

 

 

 

 

Vref

 

 

 

 

 

 

 

 

 

 

 

 

 

Quadrature-nulling,

 

Vp Zt

 

 

 

 

 

 

Vs + n

two-phase LIA

 

 

 

 

Vϕ Zt

 

 

 

 

 

 

 

 

 

 

 

 

FIGURE 12.51

An impedance plethysmograph in which a constant ac current is passed through the body part being studied. A self-nulling, two phase lock-in amplifier is used to output voltages proportional to the impedance magnitude and angle. These voltages can be used to generate a polar plot of Zt.

pressure at a given sinusoidal frequency. Acoustic impedance has been used experimentally to try to diagnose obstructive lung diseases, as well as problems with the eardrum and middle ear (Northrop, 2002). This section describes the electronic circuitry associated with a simple prototype acoustic impedance measurement system. Figure 12.52 illustrates an electric circuit that is an analog of the acoustic system used to measure the complex acoustic impedance vector looking into the respiratory system through the mouth. Note that phasor sound pressure levels P1 and P2 are analogous to voltages; acoustic resistance, Rac, and complex acoustic impedance, Zac(jω), are analo-

gous to electrical resistance and impedance; and the complex volume flow · ω ω

rate, Q2(j ), is analogous to the phasor electrical current, I2(j ). Thus, by the “acoustical Ohm’s law”:

˙

(jω) = (P1 P2 )

Rac = P2 Zac (jω)

(12.131)

Q2

Thus,

 

 

 

 

 

Zac (jω) =

P2Rac

 

cgs acoustic ohms

(12.132)

(P1 P2 )

 

 

 

 

© 2004 by CRC Press LLC

Examples of Special Analog Circuits and Systems

535

 

 

 

DA1

VQ Q2

 

 

 

 

V2 P2

 

 

DA2

 

Rac

 

P1

P2

 

 

 

 

Q2

 

P1

Zac(jω)

 

FIGURE 12.52

Electric circuit analog of the system used by the author to measure the acoustic impedance, Zac(f), of the respiratory system. In the circuit, voltage is analogous to pressure and current is analogous to volume flow.

Assume that a microphone output voltage is proportional to the incident acoustical sound pressure, i.e., V2 = Km P2, V1 = Km P1. Thus, the vector Zac() can be found by substituting the conditioned microphone voltages into Equation 12.132.

Figure 12.53 illustrates the system devised by the author to measure Zac() in polar form — i.e.,

Vθ Zac () = −–(V1 V2 ),

(12.133)

and

 

 

 

 

 

 

 

Zac ()

 

 

 

V2

 

Rac

(12.134)

 

 

 

 

 

 

 

 

 

 

V1 V2

 

 

 

 

 

 

 

where the angle of V2 is taken as 0 (reference).

Note that the angle between V1 and V2 (P1 and P2) is measured by passing these sinusoidal voltages into voltage comparators serving as zero-crossing detectors producing 50% duty cycle TTL waves with the same phase difference as the analog V1 and V2. The TTL phase difference is sensed by a digital phase detector of the MC4044 type (see Section 12.3.3), giving a dc output, Vθ. Simultaneously, the ac voltages (V1 V2) and V2 are converted to their dc RMS values, VQ and VP, respectively. Vθ, VP, and VQ are sampled and converted to digital format and passed through a computer interface. The computer calculates and displays:

© 2004 by CRC Press LLC

536

Analysis and Application of Analog Electronic Circuits

 

OXD

 

 

 

 

Comp

 

 

LPF

 

 

TTL

 

Vθ

 

 

PD

(dc)

 

OXD

 

 

 

 

 

 

 

Comp

 

 

 

 

V1

 

 

To

PRA

(ac)

TRMS

 

ADCs

 

 

 

VQ

 

 

 

 

 

 

 

 

DA

 

 

 

 

(dc)

 

V2

 

 

VP

PRA

(ac)

TRMS

 

 

 

 

 

 

 

 

 

(dc)

 

 

Microphones

 

 

 

 

 

Acoustic

Loudspeaker

 

 

 

insulation

(not to scale)

 

 

 

 

 

 

Q

P1

P2

 

Mouthpiece

Acoustic resistance

(stack of 7 slits)

VC f

POA

VFC

From

DAC

FIGURE 12.53

Block diagram of the RAIMS system developed by the author. Infrasound pressure between 0.3 to 300 Hz was introduced into the trachea and lungs through the mouth. Output signal processing by computer allowed display of Zac(f ) in polar form over this frequency range.

 

Zac (jω)

 

= Kz

 

 

V2

Rac

(12.135)

 

 

 

 

 

 

 

V V

 

 

 

 

 

 

 

 

 

 

 

 

1

2

 

 

and

 

 

 

Zac (jω) = −Kθ (V1 V2 )

(12.136)

as a polar plot for the range of frequencies used.

An 8-in. loudspeaker drove the acoustic resistance chamber. The loudspeaker was driven by a power amplifier with sinusoidal input from a VFC. The VFC, in turn, got its dc input voltage, VC, from an 8-bit DAC with input from the computer.

© 2004 by CRC Press LLC