Q14: LOCK IN AMPLIFIER APPLICATION Bentley, Part A The block diagram in Figure 1 below describes a measurement system ba

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Q14 Lock In Amplifier Application Bentley Part A The Block Diagram In Figure 1 Below Describes A Measurement System Ba 1 (162.3 KiB) Viewed 40 times

Q14: LOCK IN AMPLIFIER APPLICATION Bentley, Part A The block diagram in Figure 1 below describes a measurement system based on a lock-in amplifier configuration. A linear resistive transducer (RT) is used to provide an indirect measurement of the temperature (T). The transducer has been calibrated at room temperature TO=20 °C, so that RT=RO+b(T-TO), where b=500 g/°C, RO is 1000 Q. An inverting amplifier is used to boost the signal from the transducer, where RF is 2000. RE www Transducer Bandpass filter Vbp n Vout Lowpass Mixer filter To ADC Vpsd Vdc Ry VN Figure 1 Q14A) Derive the algebraic equation that describes the output of the first amplifier stage Vout. For this consider an ideal Opamp with infinite gain AV. The input signal Vin is a sine wave signal which has amplitude 500 mV, a carrier frequency of 30 kHz and phase 0. Before the signal can be processed by the PSD (or Mixer), a bandpass filter is used to reduce the noise at the output Vout of the amplification stage. The amplification stage has a useful bandwidth of 60 kHz and 0.1 mV/Hz of input noise due to the resistive transducer. The bandpass filter transfer function is centred at 30 kHz, has a gain BP = 1 and a bandwidth of 225 Hz around 30 kHz. Q14B) Calculate the signal-to-noise ratio (SNR) of the signal Vbp at the output of the bandpass filter for T=20 °C. (Hint - you should consider that SNR = 10 logo ARMS-S ARMSN 20 logo 12v (ANS = +47.45 dB) Q14C) Derive the EXACT equation the described the signal Vpsd (at the output of the mixer) remembering that: A sin(0,1+0)* A, sin(02t+2) = 1 = $4,4, cos[w) – 0,5 +0 -0.)- 4,4, cos[wy +0,5+04+0.) After the mixer, a low-pass filter is present with a bandwidth of 1 Hz and a gain LP = 1, as represented in Figure 1. Q14D) Calculate the signal-to-noise ratio (SNR) of the signal Vdc at the output of the lowpass filter at T=20 °C. (ANS = +90.96 dB)
The system of Figure1 is used as a highly sensitive temperature sensor. Q14E) Neglecting noise contribution, calculate the value of the output Vdc if the temperature changes by 2 degrees from 20 °C to 22 °C. (ANS = +0.125 V) Q14F) Derive the algebraic equation that describes the temperature T as a function of the measured output Vdc. Q14G) Considering the four measurements provided in Table 1, Vdc Measured Values (V) 0.5 0.4 0.3 0.2 Table 1 Q14H) Plot the values of temperature obtained using the equation derived above.