12

Examples of Special Analog Circuits and

Systems in Biomedical Instrumentation

12.1 Introduction

Biomedical engineers may be expected to understand many specialized integrated circuits and be able to incorporate them effectively into biomedical measurement system designs. These integrated circuits include but are not limited to:

•Phase-sensitive rectifiers

•Phase detectors

•Voltageand current-controlled oscillators

•Phase-locked loops

•True-RMS converters

•IC thermometers

Most designers and vendors of analog ICs, such as Analog Devices, Burr–Brown, Maxim, National, etc., make one or more of the preceding ICs. In describing them, this chapter will stress application as well as design.

12.2 The Phase-Sensitive Rectifier

12.2.1Introduction

The phase-sensitive rectifier (PSR) is also known as the phase-sensitive detector, the synchronous rectifier or detector, or the balanced demodulator. Its primary role is to recover the modulating signal in a double-sideband, suppressedcarrier (amplitude) modulated carrier. The PSR is also at the heart of the lock-in amplifier, which is widely used in photonics and in certain applications

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in physics to recover a low-frequency modulating signal. A PSR will also demodulate ordinary AM. The four major embodiments of the PSR are the

(1) analog multiplier/low-pass filter (LPF) PSR; (2) switched op amp PSR;

(3) electromechanical chopper PSR; and (4) balanced diode bridge PSR. The analog multiplier PSR will be examined first.

12.2.2The Analog Multiplier/LPF PSR

Just as a DSBSCM carrier can be made by multiplying a sinusoidal carrier by the low-frequency modulating signal, the DSBSCM signal can be demodulated by multiplying the modulated carrier by a carrier frequency reference signal of the correct phase (refer to Figure 11.1B in the preceding chapter). Let the coherent modulating signal be a low-frequency sinusoid:

The reference signal is of the same frequency as the carrier but in general differs in phase by a fixed angle, (π/2 + ϕ) radians. By trigonometric identity, this is:

The analog multiplier output is:

vz (t) = {vr (t) ym (t)}10 = (VmVc Vr 20){cos[ωmt − ϕ]− cos[(2ωc + ωm )t + ϕ]+

(Note that the output of a transconductance-type analog multiplier IC is the product of the inputs divided by 10.) The unity-gain low-pass filter removes the two 2ωc terms, leaving (recall that sinθ is an odd function):

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From the trigonometric identity, {cosα + cosβ} = 2 cos[½(α + β)] cos[½(α − β)]:

In the preceding development, it was assumed that 0 < ωm ωb ωc, where ωb is the LPF’s break frequency. Note that the recovered modulating signal is maximum when the reference signal is in phase with the quadrature carrier of the DSBSCM signal. Thus, an analog multiplier can form DSBSCM signals and also demodulate them, returning a signal vm(t).

12.2.3The Switched Op Amp PSR

Figure 11.13 in Chapter 11 illustrates a PSR that uses three op amps and a digitally controlled analog MOS switch to demodulate DSBSCM signals. The MOS switch, when closed, has a very low resistance. When it is open, its resistance is on the order of megohms. The switch is controlled by the function, sgn{Vr sin(ωc t)}, which is +1 when sin(ωc t) is ≥ 0 and −1 when sin(ωc t) < 0. The output, vz(t), is a full-wave rectified ym(t), which goes negative when the sign of the modulating signal, vm(t) goes negative. It is easy to see that after low-pass filtering, vz(t) is vm(t). The average (dc value) of a full-wave rectified sine wave is πVpk/2. Note that the action of the switch effectively multiplies the DSBSCM input signal by a ±1 peak value square wave of frequency ωc/2π Hz.

12.2.4The Chopper PSR

Figure 12.1(A) illustrates the circuit of an electromechanical chopper. Electromechanical choppers are basically SPDT switches commutated by a driver coil at switching frequencies from 50 to 400 Hz or so. Developed in the WWII era as modulator/demodulators for ac DSBSCM signals, they are now obsolete. The same SPDT action can be obtained using appropriately buffered MOS switches that can be commutated in the hundreds of kilohertz or by photoelectrically turning phototransistors on and off in a photoelectric chopper. The basic electromechanical chopper uses a center-tapped signal transformer to couple the DSBSCM carrier to the switch points.

Figure 12.1(B) illustrates the raw switch output, vz(t). This signal must be low-pass filtered to recover vm(t). Note that the phase shift ϕ causes some of the chopped signal to be negative over ϕ radians of the cycle. When averaged, this negative area subtracts from the output signal. It can be shown that the phase error ϕ in the reference signal effectively multiplies the averager output by cos(ϕ). Thus, if the reference signal is 90∞ out of phase, the low-pass filtered output will always be zero.

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FIGURE 12.1

(A) Circuit of an electromechanical chopper phase-sensitive rectifier (PSR). (B) Upper waveform: chopper input. p and n denote the intervals the chopper switch dwells on the positive or minus contacts, respectively. Lower waveform: chopper output when the switch control sync voltage, vr(t), is out of phase with vm(t) by ϕ radians. Perfect full-wave rectification is not achieved.

12.2.5The Balanced Diode Bridge PSR

Still another circuit that can be used to demodulate DSBSCM signals is the balanced diode bridge PSR, illustrated in Figure 12.2. The modulated signal, ym(t), and the reference signal, vr(t), are coupled to the diode bridge by two center-tapped transformers. The transformer on the left is called the signal transformer and the one on the right is the reference transformer.

To understand how the diode bridge PSR works, refer to Figure 12.3. Assume vr(t) > 0, diodes a and b conduct current ir+, and c and d are cut off (treated as open circuits). The positive signal voltage at node B causes a current, ima and imb, to flow through diodes a and b, respectively. Assume that ima > ir+, so diode a continues to conduct. The currents ima and imb flow through both halves of the reference transformer secondary, combine, and flow to

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FIGURE 12.2

A balanced-bridge diode PSR.

B

R vz(t)

FIGURE 12.3

The diode bridge PSR when diodes a and b are conducting, and c and d are blocking current flow.

ground through the resistor R. Note that it is the top half of the signal transformer that supplies im+.

The output voltage is vo(t) = im+(t)R for positive vr(t) and positive (or negative) vm(t). During the negative half cycle of vr(t) shown in Figure 12.4, diodes c and d conduct and a and b are reverse biased. Now the lower half of the signal transformer secondary delivers signal current im− to the load R in the same direction as im+, producing phase-sensitive rectification. Note that if the phase of ym(t) changes by 180∞, the sign of the rectified vo(t) also changes, giving a negative output. The output of the balanced diode bridge PSR has a relatively high output impedance and therefore must be buffered before vo(t) is sent to a low-pass filter for averaging. The permissible upper

© 2004 by CRC Press LLC