## NEGATIVE FEEDBACK

As shown in Figure 2(d), with 10% negative feedback, the gain AV drops to half of AV. In other words, negative feedback reduces the overall gain of an amplifier. Therefore it is called degenerative feedback. Here, a portion of the amplifier output is fed back to the input in such way that it opposes the input. Consider the case when AV = AV/100. Since the gain in deci­bels is defined as 20 log10(VO/VI), the reduction of the gain by a factor of 100 means a loss of 20 log10 iio = —40 dB. Thus, expressed in decibels,

AV = AV — 40 dB

Now we can revisit Fig. 1 and study the frequency re­sponse with and without negative feedback. This is shown in Fig. 3. We can easily see that the bandwidth of the amplifier has been increased with negative feedback. This is the great­est advantage of negative-feedback amplifiers. In addition, negative feedback results in stabilized amplifier gain, ex­tended bandwidth, and reduced noise and distortion. In other words, it is possible to achieve predictable voltage gains with negative feedback amplifiers. Besides, the resulting amplifi­ers are very stable.

It is possible to prove that series voltage feedback in­creases the input impedance of the circuit. The input imped­ance can be reduced by incorporating a parallel current feedback.

We can rewrite the previously considered equation incorpo­rating the negative sign as

A’ =

V 1 + My

Without feedback

For very large values of AV the above equation becomes

1/в

Consider a case when AV2 = (1 + 0.707AV = 1.707/3. Re­calculate the new closed-loop gain with negative feedback:

V 2

Ay2 1 + M

V2

1.707/в

1 + (1.707в/в)

= 0. 707/в = 0.707AV

Observe that the above equation is independent of AV, which is the gain without feedback. (also sometimes called the open – loop gain). In other words, even though the open-loop gain falls by a factor 1.707, the closed-loop gain falls only by 3 dB. Similarly, we can prove

Percentage distortion with negative feedback

Percentage distortion without negative feedback 1 + pAv

Negative feedback also helps in reducing the circuit noise. Thus, the signal-to-noise ratio is greatly improved:

= (1 + вAv )(S/N)

## Diathermy for Musculoskeletal Conditions

Therapeutic heating of musculoskeletal tissues by conversion of electromagnetic and ultrasonic energies in deep-lying tissues without excessive heating of the skin is known as diathermy (through heat). It has been the dominant clinical application until the 1970s. Diathermy modalities in use include spot focus ultrasonic transducers that operate at 1 MHz. In the United States, the most prevalent electromagnetic modalities are the shortwave inductive-coil diathermy operating at 27.12 MHz and the microwave (corner reflector or aperture) diathermy operating at 2450 MHz. The frequency of 433 MHz is used extensively in many European countries.

In practice, clinical diathermy is guided by patient report of pain and warmth sensation. Since local elevation of tissue temperature is apparently the most significant factor in physiological response to diathermy, objective measures of subcutaneous tissue temperature in real time would enhance both its efficacy and safety. While accurate and reliable noninvasive sensing of subcutaneous temperature must await further technological advance, the combination of multiple invasive sensors and computational estimates can provide some useful information.

Therapeutic indications are based on local elevations of tissue temperature brought about by volume heating (1,2). In particular, diathermic heating to 41°C to 45°C produces hyperemia-enhanced blood perfusion to the body part under treatment. The augmentation in blood flow is accompanied by elevations in capillary pressure, in membrane permeability, and in the rate of metabolism. These increases can facilitate tissue healing and can also facilitate clearance of metabolites, debris, and toxic substances from diseased tissue under treatment. Diathermic heating of deep tissues promotes relaxation in muscles, reduces pain, and provides relief from muscle spasms (2,3). Heating can also produce greater extensibility in fibrous collagen tissues, which is significant in the management of joint contractures due to tightness of the capsule, fibrosis of muscle, and scarring.

## PRINCIPLES OF FEEDBACK

For a simple amplifier the voltage gain is defined as the ratio of output voltage to input voltage. This is written as AV = VO/VI as shown in Fig. 2(a). Addition of a feedback of magni­tude 3, as shown in Fig. 2(b), will result in a modified value for the voltage gain given by the equation: AV = AV/(1 — 3AV). The term /SAV, called the feedback factor, can be either positive or negative. A study of the variation of AV with posi­tive as well as negative values of 3 is shown in Fig. 2(c, d). It is observed that the value of AV becomes infinite with only 10% of positive feedback. However, this should not be viewed as advantageous, because positive feedback greatly increases distortion in the output. Mathematically it is true that the gain approaches infinity; however, in reality, the circuit be­gins to oscillate. Positive feedback does not find many applica­tions.

 voltage Vj

 voltage VO

 (a)

 Figure 2. (a) Block diagram of an amplifier with AV = VO/Vi. (b) Block diagram of an amplifier with feedback. The dashed line en­closes the entire amplifier including the feedback; its gain is AV = VO/Vi.

 Midfrequency level

 flat

 Vfl,

 (b)

 Figure 1. Frequency response curve of an audio amplifier.

 Consider the case when PO = JPj. Then the gain in decibels is 101og10 = -3.0103 Therefore, for audio engineers the point of interest lies where the gain falls by 3 dB. The frequencies at which this occurs are called half-power frequencies. Let the flat portion of the
 AV Av/V2 = AV-3 dB a’v AV -3 dB = A’v/V2
 With negative feedback
 Frequency (log scale) Bandwidth _________ (no feedback) Bandwidth (with feedback)
 At
 A
 (S/N )f,
 nofeedback

However, in 1932, Harry Nyquist of Bell Telephone Labo­ratories extended this theory at length and published his fa­mous paper on regenerative theory. His principles laid the foundation for the development of feedback oscillators. There­fore, positive feedback is also called regenerative feedback. While designing frequency-selective feedback circuits for audio amplifiers, one may use positive feedback either as a bass or as a treble boost.

## HYPERTHERMIA THERAPY

The normal range of body temperature of human beings is maintained at a relatively stable temperature near 37°C. Organs and tissues function most efficiently at this range. Temperature elevation even a few degrees above this norm is associated with varying levels of biological responses. Hyperthermia is the term used to describe significant departure of tissue temperature from the usual limit (40°C) encompassed by thermoregulatory activity. Its use for therapeutic purposes has expanded in recent years to include a variety of abnormal conditions. Investigations to date have shown that while hyperthermia can produce whole-body (regional) and local tissue modifications for effective therapy, temperatures at which the desired tissue response occurs vary over a wide range. Moreover, final tissue temperature is a complex function of energy deposition, blood flow, and heat conduction in tissue.

Hyperthermia has been used therapeutically very early in human history. However, aside from a few well-established medical applications, hyperthermia is still in a relatively early stage of development. Cur­rent medical applications fall into three broad categories: musculoskeletal conditions, cancer treatment, and coagulative ablation therapy. An important aspect of its development is the production of adequate tempera­ture distribution in the target tissue, superficial or deep-seated. Moreover, successful hyperthermia therapy requires not only a suitable energy source for heat production, but also an understanding of the underlying pathological condition being treated to define the critical target temperature as well as the ability to reach that tissue with the heating modality. Energy sources that can be used for hyperthermia include ultrasonic wave and electromagnetic field and radiation as well as conducted heat or convection.

## IMPEDANCE SPECTROSCOPY

As stated before tissues can be considered as composites of cells surrounded by extracellular fluids. Each cell has a cell membrane that encloses intracellular fluid and con­sists of a thin layer of lipoproteins (^6 nm). At low fre­quencies (<10 kHz) the cell membranes have relative high resistances, and the current is conducted mainly by the extracellular fluid. At high frequencies the membrane ca­pacity causes a decrease of membrane impedance so that the current flows through the cells. The electrical behavior of a cell can be modelled by a membrane capacitance par­allel to a membrane resistance in series with pure passive resistive elements, representing extra – and intracellular fluids. Coupling of several such modelled cells results in 2- or even 3-dimensional models of tissue. For the measure­ment of the frequency dependency of tissues two methods are often used, a resistance R in series with a reactance X or a conductance G parallel to a capacitance C. The com­plex impedance Z in the first approach is given by Z = R + jX. In the second approach the admittance Y is given by Y = G + jto C. As the complex impedance is the reciprocal of the admittance the following relations hold R = G/(G2 + ш2 C2) and X = – toC/(G2 + ш2 C2).

The complex series impedance (R + jX) can be visualized in a diagram, in which the real component R is plotted versus the imaginary component X. In the literature this plot is often called the Cole-Cole diagram (54). In Fig. 7 the Cole-Cole diagram is given for a single time constant, where the impedance as a function of frequency is given by

^oa

l+ja>T

with R0 the resistance at f = ro Hz and т = CR a time constant.

The diagram is a semicircle with a radius ( r), r = (R0 — Rro )/2 and points of intersection with the horizontal axis R0 and Rro.

Although the complex series impedance of tissue is often plotted as a Cole-Cole diagram, in practice most tissues are best described with a semicircle with center slightly under the horizontal axis. Changes in tissue can be caused by changes in the amount of extra – and intracellular fluid, changes in tissue composition (e. g., tissue growth, is­chemia, infarction, tumors, increase of adipose tissue) and can be measured and visualized in such plots (55, 56). This type of research is called impedance spectroscopy.