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 highamplitude bioelectric events
•
Medium-gain amplifiers (x10 to x1000)
– Recording of ECG waveforms, muscle potentials etc.
•
High-gain amplifiers (x1000 up to x106 )
– 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 Ib- and Ib+ and output load current Io
• Three types of internal resistance and capacitance
– (1) Common-mode Rcm and Ccm, referring to internal ground Vee
– (2) Differential Rdiff and Cdiff between positive and negative input
– (3) output Ro
• Internal ground reference Vee as middle of positive and negative supply
Errors through external components
• Rs 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
• Ro creates another gain error through voltage divider behavior with the load
resistance of the following stage
- In this case Rl is large enough, so the influence from Ro isn’t strong
enough
Error sources - Inverting amplifier
Errors through internal components
•
Rcm (is parallel with R1) causes small errors, as it is usually > 1000MΩ
•
Through Ccm (< 5pF) higher gain errors will be produced in higher
frequencies (Rc=1/jωc)
-Example: at 1 Mhz Ccm reactance is at 32kΩ, 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 (Rcm, Rdiff etc.).Therefore
very little gain error is induced
• Small gain error is produced by the voltage divider consisting of Ro and RL
• Furthermore additional gain errors are created through the bias currents
flowing through the feedback resistances (Ib- and Ib+)
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 Æ if=0Æ 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
Differential Gain of the two
non-inverting combined followers:
One op-amp differential
amplifier
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=2πf) 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=2πf) 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