20-Bio-B6 Analytical Biochemistry · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2014 — 04-Bio-B6 Bioinstrumentation. Three hours, open book, non-communicating calculator permitted. Six questions of equal value (25 marks each); four constitute a complete paper and only the first four appearing in the answer book are marked. All six are solved here as a complete study resource. Every question is a design/essay question (block-diagram instrumentation-system design, or descriptive explanation).
Reference texts (the books a candidate should have reviewed for this subject):
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
A piezoelectric crystal under applied force generates a charge $q=d\cdot F$ (charge sensitivity $d$, applied force $F$), so it is modelled as a charge (or current) source in parallel with its own internal capacitance $C_a$ (formed by the electroded crystal faces) and internal leakage resistance $R_a$ (very high, typically GΩ-range, representing slow internal charge decay). The connecting cable adds its own capacitance $C_c$ in parallel across the same two nodes. This RC network is fed into a charge amplifier: an op-amp in an inverting, capacitive-feedback configuration, with feedback capacitor $C_f$ and a parallel feedback (bleed) resistor $R_f$.
Each element: the charge/current source $i_p(t)=d\cdot\frac{dF}{dt}$ (equivalently $q=d\cdot F$) represents the piezoelectric effect itself — the electrical output generated by the applied mechanical force. $C_a$ is the crystal's own capacitance (a parallel-plate capacitor formed by its electroded faces). $R_a$ is the crystal's internal leakage/insulation resistance; because it is finite (though very large), charge deposited by a sustained static force slowly bleeds away, which is why a piezoelectric sensor cannot measure a true DC/static force indefinitely — only dynamic or transient forces. $C_c$ is the cable capacitance between the transducer and the amplifier, which appears electrically in parallel with $C_a$. The charge amplifier holds its inverting input at virtual ground, so essentially all of the generated charge is forced onto the feedback capacitor $C_f$, giving an output $V_{out}=-q/C_f=-dF/C_f$ that is ideally independent of $C_a$ and $C_c$ — the key advantage over a plain voltage amplifier, whose gain would depend on cable length through $C_c$. The feedback (bleed) resistor $R_f$ provides a DC path to prevent the integrator from drifting into saturation and sets the amplifier's own low-frequency (high-pass) cutoff, $f_c=1/(2\pi R_fC_f)$, below which slowly-varying force components are not faithfully reproduced.
A single piezoelectric element can serve as both transmitter and receiver by time-multiplexing the two roles through a transmit/receive (T/R) switch — the same reversibility (converse piezoelectric effect on transmit, direct piezoelectric effect on receive) named in the question stem. This is the basis of a pulsed-Doppler ultrasound flowmeter.
Transducer operation. On transmit, an electrical burst applied to the crystal makes it vibrate at its resonant frequency $f_0$ (converse piezoelectric effect), launching a short ultrasound pulse into the tissue. Immediately after the burst, the T/R switch reconnects the same crystal to the receive amplifier; returning echoes — scattered from moving red blood cells — flex the crystal and it generates a small charge/voltage proportional to the incident acoustic pressure (direct piezoelectric effect). The single element can do this because transmit and receive are separated in time, not because it does both simultaneously.
Pulser. Generates a short (few-cycle) electrical burst at the transducer's resonant frequency to drive the transmit pulse; pulse repetition frequency (PRF) is chosen high enough to satisfy the Doppler sampling requirement yet low enough that the echo from the depth of interest returns before the next pulse is sent.
T/R switch. Isolates the sensitive receive amplifier from the large transmit voltage during the burst, then connects the transducer to the receiver for the (much smaller) returning echo.
Receive amplifier + time-gain compensation (TGC). Amplifies the weak echo; TGC increases gain progressively with elapsed time since the transmit pulse to compensate for the exponential attenuation of ultrasound with depth in tissue, so echoes from deeper, weaker-signal vessels are not lost relative to shallow ones.
Range gate (depth selection). A timing circuit accepts only the portion of the returning echo arriving in a chosen time window after the transmit pulse. Because round-trip time and depth are related by $z=\frac{c\,t}{2}$ (speed of sound in tissue $c\approx1540$ m/s), gating the receiver to open only at the delay corresponding to a superficial or a deep artery lets the same transducer/beam interrogate either vessel — this range-gating is what a single-element pulsed system provides that a continuous-wave system cannot.
Quadrature demodulator. Mixes the gated receive signal with in-phase and quadrature references at $f_0$ to extract the (much smaller) Doppler-shifted frequency component and its sign, which indicates flow direction (toward vs. away from the transducer).
Doppler-shift extraction. An FFT (or zero-crossing detector, for a simpler design) of the demodulated signal yields the Doppler-frequency spectrum, from which mean and peak blood velocity are computed via $\Delta f=\dfrac{2f_0v\cos\theta}{c}$ (beam-to-flow angle $\theta$).
Display. A scrolling velocity/flow waveform (and, in a duplex system, a spectral sonogram) is shown, together with an audible Doppler tone whose pitch and character let the clinician judge flow quality by ear, as is standard clinical practice.
