Medical Instrumentation II

1. (Axial) Stress On the surface, the (average) force per unit area is denoted as σ : “Stress” (cf. pressure) M y x A Medical Instrumentation II F(force) is sometimes called “load”

2. Strain Medical Instrumentation II L(length) wall F(force) wall F(force) Strain is unitless!

3. & curve 1. Brittle material (ex. Glass) rapture Linear region : elastic region (ex. Spring) Ultimate stress After this rapture, material is broken by force and no stress & strain state Medical Instrumentation II Not linear over a wide range

2. Ductile material (ex. aluminium, steel) Medical Instrumentation II Elastic region Yield region Plastic region rapture Aluminium

Medical Instrumentation II rapture Steel Elastic region For elestic region : linear region (σ ≤ σ PL ) E : young’s modulus (modulus of elasticity)

//Summary// Medical Instrumentation II

4. Cantilever Medical Instrumentation II L(length) wall F(force) Al X X = 0 Constant E is Constant A&L are almost Constant

5. Strain gage Medical Instrumentation II Substrate Electrical wire L(length) Resistivity + - A(Surface area)

6. Partial differentiation Medical Instrumentation II

Fractional Poisson’s ratio

Medical Instrumentation II L(length) D Piezoresistive effect Dimensional effect

Medical Instrumentation II Gage factor For metal strain gage G : ~ 1.6 For semiconductor strain gage G : 100 ~ 170 (High temperature coefficient)

Problem (3) Solution.  Metal strain gage four (gage factor is 10) set up in a tool. F is authorized a tool. gage 1 & 2 are increase ΔL, gage 3 & 4 are decrease ΔL. ΔL/L = kF (k is constant). design by bridge circuit (out voltage proportionate force). Represent out voltage by force. Drive voltage is dc 5v. Medical Instrumentation II

wall F(force) wall Gage 1 & 2 : L -> L + ΔL Gage 3 & 4 : L -> L - ΔL Side view

Medical Instrumentation II wall Cf. F(force) ResistorVariable ResistorResistive Sensor

Medical Instrumentation II 5v R3 R1 R4 R2 reference in = 0 ip = 0 IA V0 = Av V0 = Av(Va – Vb) VaVb Va Vb

Medical Instrumentation II Your design Given by structure & material Part of it is your design

Problem (4) Solution.  Two p - type Si strain gage (Gage factor is +100) and two n - type Si strain gage (Gage factor is -100) use system (measure force)  (a) Bridge circuit consist of four strain gage. Design circuit that bridge’s output is amplified by instrumentation amplifier. (clear state strain gage type consist of bridge circuit) drive voltage is dc 1V.  (b) When cantilever is authorized force, cantilever’s increase & decrease length is equal. Strain gage’s maximum length rate is ±0.05%, when no load, strain gage resistance is 200Ω. Output by authorized force is change ±5v. Define instrumentation amplifier’s gain.  (c) Propose calibration method in force instrumentation. Medical Instrumentation II

wall S1 S3 S2 S4 wall S1 S3 S2 S4 E[v] S3 R1 S2 S4 reference in = 0 ip = 0 IA VaVb S1 : ∆L increase / ∆R increase S2 : ∆L decrease / ∆R decrease S3 : ∆L increase / ∆R decrease S4 : ∆L decrease / ∆R increase Gain is positive Gain is negative

Medical Instrumentation II - 5 ≤ V0 ≤ 5 [v]

Medical Instrumentation II V0 F (C) Use least square method Second & third order polinominal

Problem (6) My Solution.  Two p - type Si strain gage (Gage factor is +100) and two n - type Si strain gage (Gage factor is -100) use system (measure force). When diaphragm is authorized pressure, each strain gage generate same strain and sensitivity is 10⁻⁵ %/mmHg. when no pressure, strain gage resistance is 50Ω. (Suppose that pressure proportionate strain).  (a) When pressure changing 0 – 500mmHg, How change p & n type Si strain gage’s resistance?  (b) Draw bridge circuit consist of four strain gage. and Where are each strain gage? Mark it!  (c) drive voltage is dc 1v, Output by authorized pressure is change 0 - 1v. define instrumentation amplifier’s gain Medical Instrumentation II

(a) Strain gage pressure < X p < 500 Pressure 0 : 50 Pressure 500 : 52.5 & 47.5 Pressure & strain is linear P-type n-type

Medical Instrumentation II (b) E[v] S1 S3 S4 S2 reference in = 0 ip = 0 IA VaVb (c)

Medical Instrumentation II R is 50Ω △ L/L = G = 100 Av = 100 I’m sorry prof. woo,,,, problem is so difficult,,,