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**Op-amp Circuits and Active Filters**

Analog Electronics Lecture 7 Op-amp Circuits and Active Filters Muhammad Amir Yousaf

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**Lecture: How to compare an analog signal with certain voltage level.**

Comparing a noisy signal with certain (reference) level. Binding an signal to fixed +/- max levels. Analog to digital converters with comparators. Adding two analog signals. Adding weighted signals. Averaging on analog signals. Digital to Analog Converter with weighted additions. Integrating an analog waveform. Differentiating analog waveform. Logarithm on analog signal. Antilog of analog signal. Multiplying and diving analog signals. Converters. Peak Detectors. Filters.

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Comparators A comparator is a specialized nonlinear op-amp circuit that compares two input voltages and produces an output state that indicates which one is greater. Because of the high open-loop voltage gain, a very small difference voltage between the two inputs drives the amplifier into saturation. Zero Level Detection:

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Comparators Non-Zero Level Detection:

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**Noise contaminated signal may cause an unstable output.**

Noise on Comparator Noise contaminated signal may cause an unstable output.

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**Comparator with Hysteresis**

To avoid this, hysteresis can be used. Hysteresis is incorporated by adding regenerative (positive) feedback, which creates two switching points: The upper trigger point (UTP) and the lower trigger point (LTP). After one trigger point is crossed, it becomes inactive and the other one becomes active.

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Output Bounding Some applications require a limit to the output of the comparator (such as a digital circuit). The output can be limited by using one or two Zener diodes in the feedback circuit. The circuit shown here is bounded as a positive value equal to the zener breakdown voltage.

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**Comparator Applications**

Flash analog-to-digital converters use 2n-1 comparators to convert an analog input to a digital value of n bits for processing. Flash ADCs are a series of comparators, each with a slightly different reference voltage. The priority encoder produces an output equal to the highest value input.

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Summing Amplifier A summing amplifier has two or more inputs; normally all inputs have unity gain. The output is proportional to the negative of the algebraic sum of the inputs.

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**Example Summing Amplifier**

What is VOUT if the input voltages are +5.0 V, -3.5 V and +4.2 V and all resistors = 10 kW? 10 kW VOUT = -(VIN1 + VIN2 + VIN3) = -(+5.0 V V V) = -5.7 V

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Averaging Amplifier An averaging amplifier is basically a summing amplifier with the gain set to Rf /R = 1/n (n is the number of inputs). The output is the negative average of the inputs. What is VOUT if the input voltages are +5.0 V, -3.5 V and +4.2 V? Assume R1 = R2 = R3 = 10 kW and Rf = 3.3 kW? 3.3 kW VOUT = -⅓(VIN1 + VIN2 + VIN3) = -⅓(+5.0 V V V) = -1.9 V

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Scaling Adder A scaling adder has two or more inputs with each input having a different gain.

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**Scaling Adder: D/A Converter**

An application of a scaling adder is the D/A converter circuit shown here. The resistors are inversely proportional to the binary column weights. Because of the precision required of resistors, the method is useful only for small DACs.

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**The Integrator Vout=− 1 𝑅𝐶 0 𝑡 𝑉𝑖𝑛𝑑𝑡**

An op-amp integrator simulates mathematical integration, a summing process that determines total area under curve. IC Ii Ideal Integrator Vout=− 1 𝑅𝐶 0 𝑡 𝑉𝑖𝑛𝑑𝑡 The ideal integrator is an inverting amplifier that has a capacitor in the feedback path. The output voltage is proportional to the negative integral (running sum) of the input voltage.

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The Integrator Capacitor in the ideal integrator’s feedback is open to dc. This implies open loop gain with dc offset. That would lead to saturation. The practical integrator overcomes these issues– the simplest method is to add a relatively large feedback resistor. Rf should be large enough Practical Integrator

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**The Differentiator I= 𝑑𝑄 𝑑𝑡 =𝐶. 𝑑𝑉 𝑑𝑡 𝐶. 𝑑𝑉𝑖𝑛 𝑑𝑡 =− 𝑉𝑜𝑢𝑡 𝑅**

An op-amp differentiator simulates mathematical differentiation, a process to determine instantaneous rate of change of a function. Ideal Differentiator The ideal differentiator is an inverting amplifier that has a capacitor in the input path. The output voltage is proportional to the negative rate of change of the input voltage. I= 𝑑𝑄 𝑑𝑡 =𝐶. 𝑑𝑉 𝑑𝑡 𝐶. 𝑑𝑉𝑖𝑛 𝑑𝑡 =− 𝑉𝑜𝑢𝑡 𝑅 𝑉𝑜𝑢𝑡 = -RC. 𝑑𝑉𝑖𝑛 𝑑𝑡

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**Instrumentation Amplifiers**

An instrumentation amplifier (IA) amplifies the voltage difference between its terminals. It is optimized for amplifying small differential signals that may be riding on a large common mode voltages. High input impedance High CMMR Low output offset Low output impedance

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**Instrumentation Amplifiers**

IC of instrumentation amplifier is made up of three op amps and several resistors. The gain is set by a single resistor that is supplied by the user. The output voltage is the closed loop gain set by RG multiplied by the voltage difference in the inputs.

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**Instrumentation Amplifiers (IA)**

Applications: Used where a quantity is sensed by a remote sensor e.g. temperature, pressure transducer and sensed signal is sent over a long line. Electrical noise produces common-mode voltages in the line. IA at the end of line amplifies only the small differential signal and reject the common mode signal

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**Instrumentation Amplifiers**

Example Instrumentation Amplifiers An IA that is based on the three op-amp design is the AD622. The formula for choosing RG is: Example: What value of RG will set the gain to 35? Solution: = 1.5 kW

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**The Logarithmic Amplifier**

A logarithmic (log) amplifier produces an output that is proportional to the logarithm of the input Log and antilog amplifiers are used in applications that require: Compression of analog input data. Linearization of transducers that have exponential outputs. Analog multiplication and division, etc

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**The Logarithmic Amplifier**

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**The Logarithmic Amplifier**

A semiconductor pn-junction in the form of either a diode or the base-emitter junction of a BJT provides a logarithmic characteristic. Voltage across the diode is proportional to the log of the current in the diode. Compare data for an actual diode on linear and logarithmic plots:

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**The Logarithmic Amplifier**

When a diode is placed in the feedback path of an inverting op-amp, the output voltage is proportional to the log of the input voltage. The gain decreases with increasing input voltage; therefore the amplifier is said to compress signals. Many sensors, particularly photo-sensors, have a very large dynamic range outputs. Current from photodiodes can range over 5 decades. A log amp will amplify the small current more than the larger current to effectively compress the data for further processing.

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**The Logarithmic Amplifier**

Example The Logarithmic Amplifier For the circuit shown, the equation for Vout is (IR is a constant for a given diode.) Example: What is Vout? (Assume IR = 50 nA.) Solution: = -307 mV

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**The Antilog Amplifier x= 𝑒 𝑙𝑛𝑥 𝑉𝑜𝑢𝑡 = - 𝑅𝐹. IR 𝑒 𝑞𝑉𝑖𝑛/𝑘𝑇**

The antilogarithm of a number is the result obtained when the base is raised to a power equal to the logarithm of that number. x= 𝑒 𝑙𝑛𝑥 IR 𝑒 𝑞𝑉𝑖𝑛/𝑘𝑇 =− 𝑉𝑜𝑢𝑡 𝑅𝐹 𝑉𝑜𝑢𝑡 = - 𝑅𝐹. IR 𝑒 𝑞𝑉𝑖𝑛/𝑘𝑇

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**Constant-current source**

A constant-current source delivers a load current that remains constant when the load resistance changes. A basic circuit in which a stable voltage source (Vin) provides a constant current (Ii) through the input resistor (Ri) If RL changes, IL remains constant as long as Vin and Ri are held constant.

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**Current to Voltage Converter**

A current-to-voltage converter converts a variable input current to a proportional output voltage. A specific application of this circuit is where a photoconductive cell is used to sense changes in light level. As the amount of light changes, the cur-rent through the photoconductive cell varies because of the cell’s change in resistance. This change in resistance produces a proportional change in the output voltage.

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Peak Detector The circuit is used to detect the peak of the input voltage and store that peak voltage on a capacitor. The circuit can be used to detect and store the maximum value of a voltage surge.

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**Charge Sensitive Amplifier**

It is used in Radiation detection Charge on a photon is accumulated in the capacitor

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Active Filters

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**Basic filter Responses**

A filter is a circuit that passes certain frequencies and rejects all others. The passband is the range of frequencies allowed through the filter. The critical frequency defines the end (or ends) of the passband and is normally specified at the point where the response drops -3dB (70.7%) from the passband response. Following the passband is a region called the transition region that leads into a region called the stopband. Low-pass High-pass Band-pass Band-stop

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**The Basic Low-Pass Filter**

The low-pass filter allows frequencies below the critical frequency to pass and rejects other. The simplest low-pass filter is a passive RC circuit with the output taken across C. BW = fc

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**The Basic Low-Pass Filter**

The ideal response is not attainable by any practical filter. Actual filter responses depend on the number of poles, Pole, a term used with filters to describe the number of RC circuits contained in the filter. This basic RC filter has a single pole, and it rolls off at -20db/decade beyond the critical frequency. 20db/decade means that at a frequency of 10fc the output will be -20dB(10%) of the input. This roll-off allows too much unwanted frequencies through the filter

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**The Basic Low-Pass Filter**

Actual filters do not have a perfectly flat response up to the cutoff frequency. More steeper response cannot be obtained by simply cascading the basic stages due to loading effect. With combination of op-amps, the filters can be designed with higher roll-offs In general, the more poles the filter uses, the steeper its transition region will be. The exact response depends on the type of filter and the number of pole.

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**General Active Filters**

A single pole active filters The number of filter poles can be increases with cascading

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**The Basic High-Pass Filter**

The high-pass filter passes all frequencies above a critical frequency and rejects all others. The simplest high-pass filter is a passive RC circuit with the output taken across R.

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The Band-Pass Filter A band-pass filter passes all frequencies between two critical frequencies. The bandwidth is defined as the difference between the two critical frequencies fc1 and fc2. The simplest band-pass filter is an RLC circuit. Bandwidth B.W= fc2 – fc1 Center frequency fo= √ fc1 fc2 Quality Factor: In band pass filters it is ratio of center frequency to its bandwidth. Q = fo /B.W

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The Band-Stop Filter A band-stop filter rejects frequencies between two critical frequencies; the bandwidth is measured between the critical frequencies. The simplest band-stop filter is an RLC circuit.

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Ideal vs Real Filters In comparison to ideal low pass filters, the real RC or RLC filters lack the following characteristics: Flat passband Sharp transition region Linear phase response

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**Active filters include one or more op-amps in the design. **

One of the three characteristic can be achieved with active filters: Chebyshev: rapid roll-off characteristic Flat band pass with Butterworth Sharp roll-off rate with Chebyshev Linear phase response. Butterworth: flat amplitude response Bessel: linear phase response

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