Perceptible output Output display Control And feedback Signal processing Data transmission storage Variable Conversion element Sensor Primary Sensing Measurand Calibration signal Radiation, electric current, or other applied energy Power source Figure 1.1 Generalized instrumentation system The sensor converts energy or information from the measurand to another form (usually electric). This signal is the processed and displayed so that humans can perceive the information. Elements and connections shown by dashed lines are optional for some applications.

Electrodes vecg 60-Hz ac magnetic field + Vcc Z1 Zbody Z2 + Differential amplifier vo - Displacement currents -Vcc Figure 1.2 Simplified electrocardiographic recording system Two possible interfering inputs are stray magnetic fields and capacitively coupled noise. Orientation of patient cables and changes in electrode-skin impedance are two possible modifying inputs. Z1 and Z2 represent the electrode-skin interface impedances.

(xd – Hfy)Gd = y (1.1)   xdGd = y(1 + HfGd) (1.2) (1.3) (1.4) (1.5) (1.6) (1.7) (1.8)  

Characteristic with zero and sensitivity drift y (Output) Total error due to drift y (Output) + Sensitivity drift D y' D x'd - Zero drift D y Dy Slope m = Dxd - Sensitivity drift Dxd Intercept b + Zero drift y = mxd + b xd (Input) xd (Input) (a) (b) Figure 1.3 (a) Static-sensitivity curve that relates desired input xd to output y. Static sensitivity may be constant for only a limited range of inputs. (b) Static sensitivity: zero drift and sensitivity drift. Dotted lines indicate that zero drift and sensitivity drift can be negative. [Part (b) modified from Measurement Systems: Application and Design, by E. O. Doebelin. Copyright  1990 by McGraw-Hill, Inc. Used with permission of McGraw-Hill Book Co.]

(1.9) (1.10)   (1.11)

x1 y1 (x1 + y2) Linear Linear (y1 + y2) system system and and Figure 1.4 (a) Basic definition of linearity for a system or element. The same linear system or element is shown four times for different inputs. (b) A graphical illustration of independent nonlinearity equals A% of the reading, or B% of full scale, whichever is greater (that is, whichever permits the larger error). [Part (b) modified from Measurement Systems: Application and Design, by E. O. Doebelin. Copyright  1990 by McGraw-Hill, Inc. Used with permission of McGraw-Hill Book Co.] x2 y2 Kx1 Ky1 Linear Linear system system (a) Least-squares straight line y (Output) B% of full scale A% of reading Overall tolerance band xd (Input) Point at which A% of reading = B% of full scale (b)

(1.12) (1.13) (1.14) (1.15) (1.16) (1.17)          

Figure 1.5 (a) A linear potentiometer, an example of a zero-order system. (b) Linear static characteristic for this system. (c) Step response is proportional to input. (d) Sinusoidal frequency response is constant with zero phase shift.

(1.18) (1.19)  

Output y(t) R + + Figure 1.6 (a) A low-pass RC filter, an example of a first-order instrument. (b) Static sensitivity for constant inputs. (c) Step response for larger time constants (L) and small time constants (S). (d) Sinusoidal frequency response for large and small time constants. Slope = K = 1 x(t) C y(t) - - Input x(t) (a) (b) x(t) Log Y (jw) scale X (jw) 1 1.0 y(t) 0.707 S L wL wS Log scale w t (c) (d) f y(t) 1 0° S Log scale w L 0.63 - 45° -90° S L t

(1.20) (1.21) (1.22) (1.23) (1.24)  

Output displacement Input Force x(t) Figure 1.7 (a) Force-measuring spring scale, an example of a second-order instrument. (b) Static sensitivity. (c) Step response for overdamped case  = 2, critically damped case  = 1, underdamped case  = 0.5. (d) Sinusoidal steady-state frequency response,  = 2,  = 1,  = 0.5. [Part (a) modified from Measurement Systems: Application and Design, by E. O. Doebelin. Copyright  1990 by McGraw-Hill, Inc. Used with permission of McGraw-Hill Book Co.] y(t) Output y ( t ) 1 Slope K = Ks Input x(t) (a) (b) x(t) Y (jw) Resonance Log X (jw) scale 1 K 2 0.5 1 wn t Log scale w (c) (d) f wn y(t) Log scale w yn 0° yn + 1 0.5 2 1 1 Ks -90° 0.5 1 2 -180° t

(1.25) (1.26)   where (1.27) (1.28)

(1.29) (1.30)   (1.31) (1.32) Overdamped, (1.33) Critically damped, (1.34) Underdamped, (1.35)

and (1.36) (1.37)   (1.38) (1.39) (1.40)

Figure 1.8 Design process for medical instruments Choice and design of instruments are affected by signal factors, and also by environmental, medical, and economic factors. (Revised from Transducers for Biomedical Measurements: Application and Design, by R. S. C. Cobbold. Copyright  1974, John Wiley and Sons, Inc. Used by permission of John Wiley and Sons, Inc.)