Analytical Chemistry II L3: Signal processing (selected slides) Semiconductor devices Apart from resistors and capacitors, electronic circuits often contain nonlinear devices: transistors and diodes. The input/output voltages/currents are not linearly proportional to one another. They are used to: rectify AC signal amplify signal attenuate signal alter frequency of a signal They can be discrete or parts of integrated circuits https://www.quora.com/how-does-a-transistor-help-in-reducing-the-size-of-an-electronic-device 1
A pn junction diode Silicon (Group IV) is doped by: - Group V elements: As, Sb (n-type) - Group III elements: Ga, In (p-type) Current-voltage characteristics forward bias reverse bias holes electrons (high resistance) Conductance: 10-6 -10-8 that of forward bias - rupture of covalent bonds - acceleration by the field - production of additional electrons and holes by collision - tunneling of electrons through the junction layer Transistor It is a basic amplifying and switching device It provides an output signal with significantly greater magnitude than the input signal Bipolar junction transistors (BJTs) can be viewed as two diodes joined together 2
Examples pnp and npn junctions bipolar junction transistors alloy transistor pnp example p region in emitter is 100 more doped than n region in base n region (base) is lightly doped pnp planar transistor npn example npn Example of a circuit with transistor (common emitter) Controlling high current with low current REVERSE Majority of holes will drift through the base to the collector The number of current-carrying holes depends on the number of electrons supplied to the base Here, it is pnp transistor Some holes flow toward the base and combine with electrons FORWARD Holes accumulate at the emitter e.g. 20-200 3
Components of a typical power supply Many elements in analytical instruments use small DC voltages. The mains AC voltage needs to be lowered, rectified, regulated, and filtered. Transformer Power transformer can decrease or increase voltage provided by the power lines. The voltage across each secondary coil is: V x = V I N 2 N 1 where N 2 and N 1 are numbers of turns in the secondary and primary coils, respectively. One transformer can have multiple secondary coils. V x V I http://wonderfulengineering.com/what-is-a-transformer/ 4
Types of rectifier / filtering the output from a rectifier Diodes are used to block current in one direction while permitting it in the opposite direction. To minimize the current fluctuations, the output is filtered by placing a capacitor with a large capacitance. Charge/discharge decreases signal variations to a small ripple (mv). Oscilloscope Oscilloscopes are used to: o view the time profiles of signals from transducers o compare the relationships among repetitive forms o reveal high frequency noise It is an essential diagnostic tool in the laboratory. https://www.amazon.com/instek-gos-630fc-oscilloscope-auto-range-triggering/dp/b006wbtz7k 5
Operational amplifiers (op amps) Operational amplifiers are used to precisely measure voltage, current, and resistance. In the past they were used for summing, multiplying, differentiating, and integrating. They require a DC power supply, e.g. +PS = +15 V, -PS = -15 V. The output voltage is related to the input voltage: v o = Av s where: v s = v + v and A is open-loop gain. http://www.ti.com/amplifier-circuit/op-amps/products.html Different ways to represent operational amplifiers GND, ground 6
Internal circuitry of an operational amplifier Several transistors and resistors in one integrated circuit (IC) chip http://www.play-hookey.com/analog/op_amps/inside_741.html http://www.righto.com/2015/10/inside-ubiquitous-741-op-amp-circuits.html Operational amplifier characteristics Large open-loop gain: A = 10 4 to >10 6 High input impedance: Z i = 10 8 to 10 15 Low output impedance: Z o = 0.001 to 1 Almost zero output voltage for zero input voltage Offset voltage input voltage required to produce zero output voltage (< 5 mv) It has two inputs: inverting and noninverting The inverting input shifts AC wave by 180 degrees out of phase (pos. neg.) The noninverting input does not produce phase/polarity change 7
Output voltage 2018-03-08 Operational amplifiers in comparator mode The voltages to be compared are supplied to the two inputs. Output is given by: v o = Av s = A(v + v ) E.g.: If the limits are 13 V and A = 10 6, then if v + >v - by more than 13 V, the output is +13 V. If the limits are 13 V and A = 10 6, then if v - >v + by more than 13 V, the output is -13 V. Input voltage Operational amplifiers in voltage follower mode The voltage follower circuit addresses the problem of errors in voltage measurements. The input resistance of the meter must be higher than internal resistance of the source. Some transducers (e.g. ph electrode) have high internal resistance. Op amps have input impedances up to 10 15, and output impedances < 1. The output voltage is the same as the input voltage. The voltage follower acts as a buffer to protect high-impedance sources. The voltage follower has a unit voltage gain: v o /v i = 1 It has a high power gain: PG = P o P i = i ov o i i v i = v o 2 /Z o Z i v 2 i /Z i Z o noninverting input isolated from the output 8
Operational amplifiers in current follower mode Current follower provides almost zero resistance to the current source. Thus, it addresses the problem of errors in current measurements. The output is connected to the inverting input via a feedback resistor R f. The potential on the inverting input is almost equal to that on the noninverting input. The noninverting input is connected to the circuit common. The inverting input is at virtual common potential. Input current: i i = i f + i b The bias current (i b ) is very low (10-11 10-15 A). Hence: i i i f v v o = i i R f 0 v o = i i R f Output voltage: v o = i f R f = i i R f almost equal summing point virtual common potential = i f R f http://www.nhn.ou.edu/~bumm/elab/lect_notes/op_amps_v1_2_2.html negligible bias current Inverting voltage amplifier Current follower can be modified to make an inverting voltage amplifier. A series resistor is placed between the source and the inverting input. The input current is: i i = v i R i The output voltage is: v o = i i R f = v i R f R i The ratio R f R i tells us how many times the input voltage is multiplied. If R f = 100 k and R i = 10 k, then the gain is 10. = v i R f R i 9
Rise time and slew rate of operational amplifier Rise time is the time required for the output to change from 10% to 90%. Slew rate is the slope of the output voltage change. Typical slew rates: a few volts per microsecond. Measurement of small photocurrent using op amp (photometer) Measuring process can perturb the system under study. We need to ensure that the perturbation is very small. In current measurements, the internal resistance of the measuring device must be small. We can use current follower to measure small current of the photocell. Output voltage: V o = I f R f = I x R f Transducer current can be calculated: I x = V o /R f = kv o Nanoampere currents can be measured 10
Measurements of conductance To measure conductance, an input AC signal is supplied to the conductance cell. The output signal is rectified, filtered, and measured as DC voltage. The potentiometer R f is used for calibration vs. the standard resistor R s. Measurements of resistance Op amps can be used to measure ratio of resistances or conductances. Absorption of light by the sample can be compared with the absorption of light by the reference solution. If the resistance of photoconductive cell is inversely proportional to the radiant power P of radiation striking it, then: R = C 1 and R P 0 = C 1 P 0 where C is a constant for both conducting cells. The meter reading is: V o = M = V C P0 P i = V i P 0 C P It reveals tiny differences in the two radiant powers. 11
Analog signal vs. digital signal In modern instruments, an analog signal is often converted to a digital one. Analog domain Digital circuits are less susceptible to environmental noise. Digital signals can be transmitted with a higher degree of integrity. Digital signals can be transmitted directly to computers. Digital domain Software can then be used to extract the information from signal outputs of chemical instruments. Digital instruments use binary number system In digital systems a small positive potential (e.g. 3 or 5 V) is used to represent binary 1, and 0 V is used to represent binary 0. 12
Determining voltage pulses per unit time counting the number of electrical pulses shaper removes small background signal, and converts the large signal pulses to rectangular pulses internal clock provides a precise time interval for counting Input signal Signal shaper comparator / discriminator Output signal Digital-to-analog converter (DAC) Digital signals sometimes need to be converted to analog signals, e.g. to be displayed on analog meter displays. In weighted-resistor ladder network, the output voltage is: v OUT = V ref R f R a 1 2 3 + a 2 2 2 + a 3 2 1 + a 4 2 0 The resolution of DAC depends on the number of input bits. For example, 10-bit DAC has 2 10 or 1024 output voltages and a resolution of 1/1024. https://www.allsyllabus.com/aj/note/ece/linear_ics_and_applications/unit4/binary-weighted%20resistor%20dac.php#.wpuyoqhuauk 13
Signal 2018-03-08 Analog-to-digital converter (ADC) example of staircase ADC The output from most transducers is analog signal. To enable computer data processing, it must be converted to a digital form. A counter and a DAC generate a staircase profile. Each step corresponds to a voltage increment (e.g. 1 mv). The output of the DAC is compared with the unknown input v i. When the two voltages are identical, the comparator changes from LO to HI, and stops the counter. The count N corresponds to the input voltage. The circuit is reset to start the next measurement. The higher the resolution of DAC, the more precisely the number will represent v i. Nyquist sampling theorem The sampling rate must be at least 2f max, or twice the highest analog frequency component. Sampling at 1 time per cycle Sampling at 1.5 times per cycle Sampling at 2 times per cycle Time Time Time http://whatis.techtarget.com/definition/nyquist-theorem https://users.cs.cf.ac.uk/dave.marshall/multimedia/node149.html 14