Operational amplifiers Types of operational amplifiers (bioelectric amplifiers have different gain values) • Low-gain amplifiers (x1 to x10) – Used for buffering and impedance transformation between signal source and readout device – Applications are measurement of action potentials and other high- amplitude bioelectric events • Medium-gain amplifiers (x10 to x1000) – Recording of ECG waveforms, muscle potentials etc. High-gain amplifiers (x1000 up to x10 6 ) • – Sensitive measurements, like recording EEG (brain potentials)
Operational amplifiers Circuit symbol of the operational amplifier Vout=Aol(Vin(+)-Vin(-))
Operational amplifiers Behavior of op-amps • Output voltage can be in range from negative to positive supply voltage - Rail-to-rail ops allow widest voltage range (nearly up to supply voltage) - Normal op-amps have lower output voltage range • The (-) input produce an output signal that is 180º out of phase with the input signal • The (+) input produce an output signal that is in phase with the input signal • No current flows in to either input terminal of the op amp (infinity Input impedance ) • Op amp with negative feedback works as an amplifier (the two input terminals are at the same voltage) • Op amp with positive or no feedback works as a comparator
Operational amplifiers Attributes of ideal op-amps • Open-loop Gain is infinite • No offset voltage • Input impedance is infinite (acts as an idea voltmeter) - bioelectric amp must have very high input impedance because all the bioelectric signal source exhibit a high source impedance • Output impedance is zero (acts as an idea voltage source) • Zero noise contribution • Bandwidth is infinite (no frequency-response limitations, no phase shift)
Basic amplifier configurations Basic amplifier configurations • Inverting amplifier or follower • Non-inverting amplifier or follower • Summing amplifier • Differential amplifier • Transimpedance amplifier (amplifies and converts input current to output voltage)
Inverting amplifier or follower •
Inverting amplifier or follower • The input-output plot of an inverting amplifier (fig) • Linearity over a limited range of Vin • The op amp is saturated at ± 13V (further increase in Vin no change in Vout)
Inverting amplifier
Error sources - Inverting amplifier Fig. 7-4 shows detailled circuit of an inverting amplifier • Bias currents I b- and I b+ and output load current I o • Three types of internal resistance and capacitance – (1) Common-mode R cm and C cm , referring to internal ground V ee – (2) Differential R diff and C diff between positive and negative input – (3) output R o • Internal ground reference V ee as middle of positive and negative supply Errors through external components • R s creates a 0.5% gain error (from the ideal -1V/V), Rs becomes part of a voltage divider with R1 at the input. -This small error can sum up in multiple staged amplifiers • R o creates another gain error through voltage divider behavior with the load resistance of the following stage - In this case R l is large enough, so the influence from R o isn’t strong enough
Error sources - Inverting amplifier Errors through internal components • Rcm (is parallel with R1) causes small errors, as it is usually > 1000M Ω • Through C cm (< 5pF) higher gain errors will be produced in higher frequencies (Rc=1/j ω c) -Example: at 1 Mhz C cm reactance is at 32k Ω , which shunts the external resistance, therefore creating a higher gain error Other errors • Bias current Ib- (nA-fA) creates a voltage at the feedback resistor which shows up at the output -In values: Ib- = 10nA, therefore 0.1 mV across R2, with Eout = 10V that means an error of 0.001%; therefore the error is rather small in this case
Non-inverting amplifier or follower • Unity gain non-inverting amp is used as a Buffer • And for impedance matching between a high source impedance and a low-impedance input circuit
Non-inverting amplifier or follower • Input - Output characteristic of a non-inverting amplifier
Non-inverting amplifier
Non-inverting amplifier and errors Details in circuit displayed in fig 7-8 • Input signal drives very high internal impedance (R cm , R diff etc.).Therefore very little gain error is induced • Small gain error is produced by the voltage divider consisting of R o and R L • Furthermore additional gain errors are created through the bias currents flowing through the feedback resistances (I b- and I b+ ) Bias currents correlate to ambient temperature • Fig 7-10 provides an overview concerning the influence from ambient temperature to bias current
Non-inverting amplifier Example • ph probe amplifier
Summing amplifier •
Summing amplifier • It is used to remove undesirable dc voltage from a signal. Vo=0 � if=0 � ij+ib=0
Differential amplifier • Produces an output voltage proportional to the difference between the voltage applied to the two input terminals • The voltage gain is the same as for inverting followers when the ratio of feedback resistor to input resistor is equal at both terminals. • Unity gain when all four resistor are equal • Removes common-mode noise and amplifying the differential signal. U3 U4 One op-amp differential amplifier
Differential amplifier • The input resistance of one op amp differential amplifier is to low for high-resistance source. Satisfactory for low-resistance source such as Wheatstone bridge • Solution: add two non-inverting gain followers of high input resistance • Instrumentation amp has also higher gain One op-amp differential amplifier Differential Gain of the two non-inverting combined followers: Three op-amp differential amp or Instrumentation amplifier
Instrumentation Amplifier
Sensors and Op-amp Examples
Transimpedance amplifier • current to voltage converter • A positive input current pulse produces a negative output voltage • The If is almost equal to Iin since Ib is small • Example (fig): 10nA input gives 0.1V output • Most common bioelectric amp is the photodiode amplifier
Integrator - a low pass filter • Gives as an output the integral of an input • When a voltage is applied to the integrator, a current I2 begins to charge C1. • It is function as a low-pass filter with frequency response: • The gain decreases as f (f=2 π f) increases
Differentiator - a high pass filter • Gives as an output the differential of an input • It is function as a high-pass filter with frequency response: • The gain increases as f (f=2 π f) increases Input Output
Active filters Frequency Response:
Comparators • Compares the input voltage with some reference voltage and gives in the output positive or negative saturation limits of the op-amp
Comparators
Schmitt Trigger Comparator
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