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 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 supplyErrors 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 amplifierand 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 fromambient 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.

One op-amp differential amplifier

U4

U3

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