--- title: "Electrode theory and ultrasonic bloodflow meter" subject: "Biomedical Instrumentation" chapter: 2 key: "semester_7/biomedical_instrumentation:electrode-theory-ultrasonic-flowmeter" source: https://www.bctengineer.com/q/semester_7/biomedical_instrumentation/electrode-theory-ultrasonic-flowmeter site: BCT Engineering --- # Electrode theory and ultrasonic bloodflow meter Biomedical Instrumentation · Chapter 2: Bioelectric Signals and Electrodes - Asked in: 2075 Chaitra, 8 marks - Video: [EE372 BIOMEDICAL INSTRUMENTATION: Bio potential Electrodes](https://www.youtube.com/watch?v=dJmsFXb3vtw) — EMPOWER - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/biomedical_instrumentation/electrode-theory-ultrasonic-flowmeter - Whole chapter: https://www.bctengineer.com/md/semester_7/biomedical_instrumentation/chapter-2 ## Question Describe electrode theory. Draw an equivalent circuit of both electrode and transducer. What type of transducer is used in ultrasonic bloodflow meter? Explain its function with necessary diagram. ## Short answer Electrode theory describes the metal-electrolyte interface where a double layer forms, creating a half-cell potential; non-polarizable Ag/AgCl electrodes minimize noise. The electrode equivalent circuit includes half-cell potential (Ehc), double-layer resistance (Rd) and capacitance (Cd) in parallel, plus series resistance (Rs). A transducer acts as a voltage source (Vs) with source impedance (Zs). Ultrasonic blood flow meters use piezoelectric crystal transducers that transmit and receive ultrasound; Doppler shift (fd = 2f0v cosθ/c) from moving red blood cells is detected to measure flow velocity. ## Answer #### Electrode theory An electrode is a conductor (metal) that connects the body (ionic conduction) with the electronic instrument (electronic conduction). When a metal is placed in an electrolyte (body fluid), a layer of ions forms: - Metal atoms dissolve as ions into the solution, leaving electrons in the metal; or ions from the solution deposit on the metal. - A **double layer of charge** (Helmholtz layer) forms at the interface and produces a potential difference called the **half-cell potential** (Ehc), e.g. about +0.223 V for Ag/AgCl. It depends on the metal and on the electrolyte concentration. - When current flows, the electrode is **polarised**: its potential moves away from the equilibrium value, causing an overpotential and noise. Non-polarisable electrodes such as silver–silver chloride are used for bio-potentials because their polarisation is very small. #### Equivalent circuit of an electrode ```text Rd +---[ ]---+ o---[Rs]----+ +----(+ Ehc -)----o to amplifier skin/ +----||----+ electrolyte Cd (Rd parallel Cd) ``` Ehc = half-cell potential (series DC source); Rd and Cd = resistance and capacitance of the double layer (polarisation impedance), connected in parallel; Rs = series resistance of the electrolyte and the leads. #### Equivalent circuit of a transducer ```text Thevenin form: [Vs]--[Zs]----o--------> to amplifier input | Zin gnd ``` A transducer acts as a signal source Vs with a source impedance Zs (resistive, capacitive or inductive). The amplifier input impedance must be much greater than Zs to avoid loading. #### Transducer in ultrasonic blood flow meter A **piezoelectric crystal transducer** (PZT or quartz) is used. As a transmitter it converts electrical energy into ultrasonic waves, and as a receiver it converts the returning echoes back into electrical signals. #### Function (Doppler flowmeter) ```text [Master oscillator 5-10 MHz] -> [RF amp] -> (Tx crystal) | ) beam | v | skin ===== vessel (blood, v) | ^ echo v ( [Demodulator] <- [RF amp] <------------------(Rx crystal) | [Audio amp] -> speaker / recorder (flow) ``` The transmitted beam, at angle θ to the vessel, is reflected by the moving red cells with a Doppler shift: **fd = 2 f0 v cos θ / c** where f0 is the transmitted frequency, v the blood velocity and c the speed of sound in tissue (about 1540 m/s). The receiver mixes the echo with the oscillator signal, giving fd (typically 1 to 15 kHz, which is audible). fd is proportional to velocity, and flow Q = v × area. The direction of flow can be found with a quadrature detector. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How does the half-cell potential arise at an electrode-electrolyte interface? A. From a double layer of charge formed at the interface as ions exchange between metal and solution B. From the amplifier input bias current C. From the body temperature gradient D. From the movement of blood past the electrode Answer: A. Ions dissolve or deposit at the metal surface, forming a double (Helmholtz) layer that gives a potential difference, Ehc. (Key point: Half-cell potential) 2. Why is Ag/AgCl preferred for recording bio-potentials? A. It has the highest polarisation so it blocks DC B. It is non-polarisable, so polarisation overpotential and noise are very small C. It has zero half-cell potential for all electrolytes D. It is cheaper than any other metal Answer: B. Ag/AgCl shows very little polarisation under current flow, so it gives low noise and stable potentials. (Key point: Non-polarisable electrode) 3. In the equivalent circuit of an electrode, what do Rd and Cd represent? A. Resistance of the leads B. The amplifier input impedance C. Resistance and capacitance of the double layer (polarisation impedance) D. The half-cell potential Answer: C. Rd in parallel with Cd models the double layer; Rs is the series electrolyte/lead resistance and Ehc is the series source. (Key point: Electrode equivalent circuit) 4. Which transducer and relation are used in the ultrasonic (Doppler) blood flow meter? A. Strain gauge; fd = f0 v / c B. Piezoelectric crystal; fd = 2 f0 v cos(theta) / c C. Thermistor; fd = f0 / v D. Photodiode; fd = c / (2 f0 v) Answer: B. A piezoelectric crystal transmits and receives; the Doppler shift is proportional to blood velocity, fd = 2 f0 v cos(theta)/c. 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