The operational amplifier circuit configurations which can perform mathematical operations such as log and antilog (exponential), including an amplification of the input signal provided to the circuit, are known as Logarithmic amplifier and Antilogarithmic amplifier respectively. In this section, we are going to learn about the Logarithmic amplifier and Antilog in detail.
An operational amplifier in which the output voltage of the amplifier (V0) is directly proportional to the natural logarithm of the input voltage (Vi) is known as a logarithmic amplifier. Basically, the natural logarithm of the input voltage is multiplied by a constant value and produced as output.
Log Amplifier Circuit
Log Amplifier Using Transistor
Log amplifier using Transistor
Log Amplifier using Diode
Log amplifier using Diode
Output and Working Principle of Log Amplifier
This can be expressed as follows:
Where K is the constant term, and Vref refers to a normalization constant, which we get to know in this section.
Generally, logarithm amplifiers may require more than one op-amp, in which case they are known as compensated logarithm amplifiers. They even require high performing op-amps for their proper functioning, such as LM1458, LM771, and LM714, are being some of the widely used logarithm amplifier.
The diode is connected in forward biasing. So, the diode current can be represented as:
Where Is is the saturation current, VD is the voltage drop for the diode. The VT is the thermal voltage. The diode current can be rewritten with high biasing condition,
The i1 expressed by,
Since the voltage at inverting terminal of the op-amp is at virtual ground, hence, the output voltage is given by V0 = -VD
Noting that i1 = iD, we can write
But, as noted earlier, VD = -V0 and so,
Taking natural logarithm on both sides of this equation, we found
Or,
The equation of the output voltage (V0) of the logarithm amplifier contains a negative sign, which indicates that there is a phase difference of 180 o. Or,
A more advanced one utilize bipolar transistors to remove Is in the logarithmic term. In this type of logarithm amplifier configuration, the output voltage is given as:
Applications of the logarithmic amplifier
Log amplifier is used for mathematical applications and also in different devices as per their need. Some of the applications of the log amplifier are as follows:
Log amplifiers are used for mathematical applications, mainly in multiplication. It is also used in the division and other exponential operations too. As it can perform multiplication operation, hence it is used in analog computers, in synthesizing audio effects, measuring instruments that require multiplication operation such as in calculating power (multiplication of current and voltage).
As we know that when we need to calculate the decibel equivalent of a given quantity, we require the use of a logarithmic operator, and hence, log amplifiers are used to calculate decibel (dB) value of a quantity.
Monolithic logarithmic amplifiers are used in certain situations, like in Radio Frequency domain, for efficient spacing (reducing components and space needed by them), and also to improve bandwidth and noise rejection.
It is also used in different ranges of applications such as rot mean square converter, an analog-to-digital converter, etc.
What is Antilog?
Antilog Amplifier
An Op-amp in which the output voltage of the amplifier (V0) is directly proportionate to the anti-log of the input voltage (Vi) is known as an anti-logarithmic amplifier or anti-log amplifier. Here, we are going to discuss the operational amplifier configuration that forms the anti-logarithmic amplifier in detail.
In the antilog amplifier, the input signal is at the inverting pin of the operational amplifier, which passes through a diode.
Antilog Amplifier using Diode
Output and Working Principle of Antilog Amplifier
As observed in the circuit shown above, the negative feedback is achieved by connecting the output to the inverting input terminal. According to the concept of the virtual ground between the input terminals of an amplifier, the voltage V1 at the inverting terminal will be zero. Because of ideally infinite input impedance, the current flowing through the diode due to the applied input voltage in the inverting terminal will not enter the op-amp; instead, it will flow along the feedback path through the resistor R as shown in the figure.
The compliment or inverse function of the logarithmic amplifier is ‘exponential’, anti-logarithmic or simply known as ‘antilog’. Consider the circuit given in the figure. The diode current is
Where, VD is the diode voltage. According to the concept of virtual ground, V1=0 as the non-inverting terminal is grounded as shown in the figure. Therefore the voltage across the diode can be expressed as VD = Vi – V1 or VD = Vi Hence, the current through the diode is
Due to the ideal characteristics of an op-amp (infinite input impedance), the current flowing through the diode ( iD) flows along the feedback path through the resistor R, as we can observe in the figure.
Therefore iD = i2
And, V0 = -i2R = -iDR
Replacing iD in the above equation we get
The parameters n, VT and IS are constants (they are only depend on the diode characteristics which are always constant for a particular diode). Therefore if the value of the feedback resistor R is fixed, then the output voltage V0 is directly proportional to the natural anti-logarithm (exponential) of the applied input voltage Vi. The above equation then can be simply represented as
Where K = – ISR and a =
Therefore we can notice that the anti-logarithmic op-amp produces its output signal as the exponential value of the input voltage signal applied.
The gain of the anti-log amplifier is given by the value of K that is equal to -ISR.
The –ve sign point out that there is a phase difference of 180degrees between the applied input s and the output of the anti-log amplifier.
A summing-amplifier is one of the op-amp applications, which performs summation or addition operations. Multiple input voltages are supplied into the amplifier, and the output provides an amplified summation of the voltages. Summing-amplifiers has various applications in electronics. It also has two types – inverting summing-amplifier and non-inverting summing-amplifier. In detail, we will discuss the analysis of the summing-amplifier in the following article.
A summing-amplifier can be defined as An amplifier, which takes multiple inputs at one of the input terminals and provides the weighted sum of all the inputs.
Non inverting summing amplifier using op amp
Non-inverting summing-amplifier is one of the types of summing-amplifiers. In this type of operations, the input voltages are provided in the amplifier’s non-inverting terminal. The polarity of the output remains the same as the inputs and because of this, it is termed as non-inverting summing-amplifier.
Inverting summing amplifier
Inverting summing-amplifier is another type of summing-amplifier where the input voltages are provided in the inverting terminals. The polarity of the output voltages gets changed and for that reason it is known as inverting summing-amplifier.
Summing amplifier design
A summing-amplifier is designed with the help of a basic op amp and resistances. It can be designed in two main configurations
inverting summing-amplifier.
non-inverting summing-amplifier.
We will discuss the general designing of a summing-amplifier.
To design a circuit with an op-amp, we have to keep in mind the op-amp’s basic properties. They are – high input impedance and the concept of virtual ground. For the virtual ground, we have to make a ground connection in any input terminal (the conventional way is to connect the ground in the opposite terminal where inputs are not supplied). A feedback path is created, keeping in mind the high input gain. Generally, a negative feedback path is made for system stability. The Inputs are provided with resistances. The output is collected from the output, containing the weighted sum of input.
Summing amplifier circuit | Op amp summing amplifier circuit design
The below images represent circuit diagrams of the summing-amplifier. The first one is for inverting the summing-amplifier circuit, and the second is for the non-inverting summing-amplifier circuit.
Observe both the circuit diagram as you can observe the difference in applying the input voltages.
Summing amplifier with ac and dc input
A summing-amplifier can be provided with either ac voltage or dc voltage. The input voltage types generally have no in the operation of the amplifier.
Summing amplifier output
The output of a summing-amplifier provides the amplified added up input voltages provided at one of the op amp input terminals. The polarity of the output voltage depends on selecting the input terminal and if the input is provided in the non-inverting terminal, the output will not be inverted. Still, if the input is provided in the inverting terminal of the circuit, there will be a polarity change.
Summing amplifier waveform
The input and output voltages of an op-amp can be observed and measured using a CRO. The CRO pins are connected with the input pins and the ground for observing the input voltages.
Summing-amplifier output waveform
To observe the output, the positive jack of the CRO is connected to the output pin, and the Negative jack is connected to the ground pin. Then we can observe the output voltage.
Gain of a summing-amplifier
The summing-amplifier is also a typical op-amp. It also amplifies the input signal and provides the output. Now, a summing-amplifier also performs the addition operation. So, it amplifies the summed-up input voltage. The general equation (of non-inverting summing amplifier) can be written as: Vo = k (V1 + V2 + … + Vn). Here, Vo is the output equation and V1, V2 … Vn are the input voltages. ‘k’ is the gain factor.
How to determine the output voltage of the summing-amplifier?
A few steps are to be followed to determine the O/P voltage of the summing-amplifier. At first, we have to use the concept of virtual ground. Using this, we make sure that voltages at both the input terminal are equal. Then apply Kirchhoff’s Current Law to get the voltage equations from the input terminals. After that, replace the necessary terms to get the final output in input voltages and resistances. Derivations for both the inverting and non-inverting types are given below.
Summing-amplifier derivation
The derivation of the summing-amplifier refers to the output equation’s derivation. The derivation includes finding out the current equation using KCL and using the concept of virtual ground ad high input impedance wherever applicable. The derivation of inverting and non-inverting summing-amplifier is done below.
Inverting summing amplifier formula
Let us determine the output formula for an inverting summing-amplifier, having ‘n’ number of inputs. Observe the circuit diagram given above.
Using the virtual ground concept, the A node’s potential is identical to potential at the B node. Applying KCL, current will be
Observe the circuit diagram of the non-inverting summing-amplifier. The feedback resistance is given as Rf. The resistances for every input voltage are assumed as R1 =R2 = R3 = R. The resistance for inverting summing-amplifier is R1. Using, the concept of virtual ground and KCL, the output equation comes as: Vo = [1 + (Rf/R1)] * [ (V1 + V2 + V3)/3]
Summing-amplifier gain formula
The output equation of an inverting summing-amplifier is given as:
Vo = – [(V1*Rf/R1) + (Rf*V2/R2) + … + (Rf*Vn/Rn)
Assuming R1 = R2 = … = Rn,
Vo = – [(V1*Rf/R1) + (Rf*V2/R1) + … + (Rf*Vn/R1)
Or, Vo = – (Rf/R1) [ V1 + V2 + … + Vn]
Now, the General equation of an inverting amplifier is:
Vo = – k (V1 + V2 + … + Vn), Where k is the gain.
So, k = (Rf/R1)
It is the gain factor of an inverting summing-amplifier.
Summing-Amplifier IC
There is no readymade summing-amplifier available in IC packaging. They are build using the conventional op-amp ICs. Op-amps, like LM358, which has a dual op-amp implemented in it, are used to make the circuit.
Summing amplifier schematic
The schematic diagram of the summing-amplifier is given below.
Schematic of internal Circuits
Analog summing-amplifier
The amplifier is an analog device. A summing-amplifier is also used for digital to analog conversion. That is why summing-amplifiers are called analog summing amplifiers.
Summing and difference amplifier theory
The theory behind summing and difference amplifier is just the mathematical operations of addition and subtraction. In the summing-amplifiers, input voltages are provided at one end, and the output, the sum of the voltages, is received with some amplification in the output.
Same for difference amplifier, two or more voltages are provided at the input stage, and an output, the difference between them is provided with amplifications.
Both the amplifiers are also basic op-amps. So, the theory and principles of basic op-amps are also followed.
Summing amplifier uses
A summing-amplifier is a handy device. As the name recommends, the amplifier mixes up signals as required. Some of the significant applications are-
Audio Mixer: Summing-amplifiers are used in audio mixing for adding up various inputs with equal gains.
DAC: Summing-amplifiers are also used in Digital to Analog Converters.
Analog Signal Processing: Summing-amplifiers are efficient instruments for signal processing.
Audio summing amplifier
Audio summing-amplifier is one of the significant applications of summing-amplifiers. Audio amplifiers mix up vocals, drums, guitars and other sounds from other instruments. It is one of the essential devices for playback recordings.
DC summing-amplifier
The Dc summing-amplifier is referred to as the summing-amplifiers fed with the input dc voltages. In general, summing-amplifiers can be fed with either ac or dc voltages for their operation.
Difference between inverting and non inverting summing amplifier
Inverting and non-inverting summing-amplifiers are nothing but two different summing-amplifiers configurations and comparison in-between as follows:
Subject of Comparison
Inverting Summing-Amplifier
Non-inverting Summing-Amplifier
Input
Input is applied in the inverting terminal of the circuit.
Input is applied to the non-inverting amplifier of the circuit.
Output
The output polarity gets inverted from the input.
The output polarity remains the same as the input terminal signal.
Preferences
An inverting summing-amplifier is more preferred comparatively.
A non-inverting summing-amplifier is used in specific applications.
Differential summing-amplifier
A summing-amplifier provides an output that includes the weighted sum of inputs. Now, suppose the output of a summing-amplifier has both the negative polarity input and positive polarity voltages. In that case, that summing amplifier will be known as a differential summing-amplifier. Such amplifiers can be designed and are readily available in the market.
Digital to analog converter summing-amplifier
A digital to analog converter converts the provided digital signal into its equivalent analog signal and to know more about digital to analog converter, Click Here.
A summing-amplifier is an essential device for making a digital to analog converter, circuit diagram of a 3-bit DAC using a summing-amplifier has been shown here.
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The output of the circuit comes as: Vo = -R [(V2/R) +(V1/2R) + (V0 / 4R)]
After simplifying the equation, we can write –
Vo = -1/4[ 4V2 + 2V1 + V0]
The output table
V2
V1
V0
Digital Value
Vout (Analog Value)
0
0
0
0
0
0
0
1
1
-0.25
0
1
0
2
-0.5
0
1
1
3
-0.75
1
0
0
4
-1.0
1
0
1
5
-1.25
1
1
0
6
-1.5
1
1
1
7
-1.75
Function of summing-amplifier
The summing-amplifier’s function is to add all the input voltages provided at either inverting or non-inverting terminal and provided the output, which contains the weighted sum of all the input.
How does a summing-amplifier work
The working of a summing-amplifier is straightforward. Inputs are given at one of the input terminals. The resistances add weight to the input voltages. The amplifier then sums up all the weighted input and produces output.
Summing-amplifier dc offset
A summing-amplifier is supplied with a DC offset voltage with an AC voltage. This supply helps maintain the LEDs in the LED modulation circuit, working in a linear range.
Summing-amplifier example
Some of the examples of summing-amplifiers are Audio mixers, Digital to analog converters, LED modulations, voltage adder, etc.
Summing scaling and averaging amplifier
Inverting amplifier has three types of configurations. They are – summing, averaging, and scaling. We have discussed inverting the summing-amplifier. Now we are going to describe the scaling and averaging.
The output equation of the inverting summing-amplifier is:
Vo = – [(V1*Rf/R1) + (Rf*V2/R2) + … + (Rf*Vn/Rn)
Now, observe. The resistance term associated with the input voltages contributes to the gain and effecting the output. Change in the resistance will change the output. This is the scaling amplifier.
Now, if (Rf / R) = 1/n, where n is the number of input, Then the equation comes as: Vo = – (1/n) [V1+ V2+ … + Vn]
We can say this equation represents the average of all the input signal. This is the averaging amplifier.
Summing-amplifier circuit on breadboard
A summing-amplifier (either inverting or non-inverting) adding up two voltages can be designed using a breadboard. The components needed for making the connections are as follow:
IC741 (1)
Multiple Voltage Source
Resistances (5kohm x 2, 1kohm x 3)
Connecting Wires
CRO
The connection is completed using the circuit diagram of the inverting summing-amplifier. The below image shows the breadboard connection of the summing-amplifier.
Frequently asked questions
1. What does a summing amplifier do
Answer: The summing-amplifier’s main objective is to add all the input voltages provided at either the inverting or non-inverting terminal and provided the output, which contains the weighted sum of all the input.
2. How does a summing amplifier work
Answer: The working of a summing-amplifier is straightforward. Inputs are given at one of the input terminals. The resistances add weight to the input voltages. The amplifier then sums up all the weighted input and produces output.
3. Summing amplifier with capacitor
Answer: Capacitors are placed in a summing-amplifier to block the signals’ Dc component. The capacitor allows only the AC parts of the incoming and outgoing signals.
4. Why is the summing op amp called a weighted summing amplifier
Answer: The summing-amplifier is often called a weighted summing-amplifier, as the output of a summing-amplifier consists of weighted input voltages. The weightage comes from the resistances connected with the input voltages.
5. What are the advantages and dis-advantage of inverting a summing amplifier
Answer: The advantages of summing-amplifier are – i) It has higher stability because of negative feedback. ii) It has three types of configurations for a summing-amplifier: summing, scaling and averaging.
The only disadvantage of the inverting summing-amplifier is that it has comparatively lower gain than the non-inverting amplifier.
6. What is the formula to calculate the value of the Rf feedback resistor in a summing amplifier circuit?
Answer: In general, Rf’s value is supplied to the circuit. If they are not available, but you have values for other parameters, you can easily find out Rf’s value from the output equation. The output equation of an inverting amplifier is given below.
Vo = – [(V1*Rf/R1) + (Rf*V2/R2) + … + (Rf*Vn/Rn)
7. Why active band stop filters are designed using a summing amplifier
Answer: Summing-amplifiers are used to design the active band stop filters as the summing-amplifier offers a linear operating region and provides the virtual ground.
The inverting operational amplifier trans impedance amplifier (TIA) is a versatile circuit that converts a current input signal into a voltage output signal. This type of amplifier is commonly used with current-based sensors, such as photodiodes, due to its unique characteristics and performance advantages. In this comprehensive guide, we will delve into the technical details, design considerations, and practical applications of the inverting operational amplifier trans impedance amp.
Understanding the Inverting Operational Amplifier Trans Impedance Amp
The inverting operational amplifier trans impedance amplifier is a specialized circuit that leverages the properties of an operational amplifier (op-amp) to perform current-to-voltage conversion. The key feature of this circuit is its ability to maintain a high input impedance, which is crucial for accurately measuring and amplifying current-based signals.
Input Impedance Characteristics
One of the most interesting aspects of the inverting operational amplifier trans impedance amp is its input impedance behavior. Algebraically, the input impedance of this circuit is found to be proportional to the frequency and resembles the impedance of an inductor. The equivalent inductance can be calculated using the formula:
L_eq = R_f / (2 * π * f)
Where:
– L_eq is the equivalent inductance
– R_f is the feedback resistor
– f is the frequency
This means that for low frequencies, the input impedance is high, while for high frequencies, the input impedance is low. This behavior can be attributed to the op-amp’s gain-bandwidth product, which determines the frequency range over which the amplifier maintains its desired characteristics.
Gain-Bandwidth Product
The gain-bandwidth product (GBW) of the op-amp used in the inverting operational amplifier trans impedance amp is a crucial parameter that affects the circuit’s performance. The gain at a given frequency is equal to the GBW divided by the frequency. This relationship is expressed as:
Gain = GBW / f
The GBW determines the frequency range over which the amplifier can maintain a stable and predictable gain. For frequencies much lower than the op-amp’s GBW, the input impedance is high, while for frequencies much higher than the GBW, the input impedance is low.
Input and Output Impedance Characteristics
The inverting operational amplifier trans impedance amp exhibits distinct input and output impedance characteristics:
Input Impedance:
At low frequencies (much lower than the op-amp’s GBW), the input impedance is high and proportional to the frequency, resembling the impedance of an inductor.
At high frequencies (much higher than the op-amp’s GBW), the input impedance is low and looks like the impedance of a resistor with a value equal to the feedback resistor.
Output Impedance:
The output impedance of the inverting operational amplifier trans impedance amp is low, similar to other op-amp-based circuits.
These impedance characteristics make the TIA a superior choice for current-to-voltage conversion compared to using a simple resistor. The high input impedance at low frequencies allows for accurate measurement of current-based signals, while the low output impedance ensures efficient signal transfer to subsequent stages.
Design Considerations for Inverting Operational Amplifier Trans Impedance Amp
When designing an inverting operational amplifier trans impedance amp, there are several key factors to consider to ensure optimal performance and meet the specific requirements of the application.
Feedback Resistor Selection
The feedback resistor, R_f, plays a crucial role in determining the overall gain and input impedance characteristics of the TIA. The value of R_f should be chosen carefully based on the following factors:
Desired Transimpedance Gain: The transimpedance gain of the TIA is equal to the value of the feedback resistor, R_f. Higher values of R_f will result in higher transimpedance gain, but may also introduce stability issues and increase the equivalent inductance of the input impedance.
Input Current Range: The maximum input current that the TIA can handle is limited by the maximum output voltage of the op-amp and the value of R_f. The maximum input current should be kept within the op-amp’s output voltage range to avoid saturation or clipping.
Equivalent Inductance: As mentioned earlier, the equivalent inductance of the input impedance is inversely proportional to the frequency and directly proportional to the value of R_f. For slow op-amps and large transimpedances, the equivalent inductance can become quite significant, which may affect the circuit’s stability and frequency response.
Op-Amp Selection
The choice of the operational amplifier used in the TIA is critical, as it directly impacts the circuit’s performance and characteristics. Key parameters to consider when selecting an op-amp include:
Gain-Bandwidth Product (GBW): The GBW of the op-amp determines the frequency range over which the amplifier maintains its desired characteristics. A higher GBW is generally preferred to extend the frequency range of the TIA.
Input Offset Voltage: The input offset voltage of the op-amp can introduce errors in the current-to-voltage conversion, especially for low-level input currents. Op-amps with low input offset voltage are preferred for high-precision TIA designs.
Input Bias Current: The input bias current of the op-amp can also contribute to errors in the current-to-voltage conversion. Op-amps with low input bias current are desirable for TIA applications.
Slew Rate: The slew rate of the op-amp determines the maximum rate of change in the output voltage, which can be important for high-speed or high-frequency TIA applications.
Noise Performance: The noise characteristics of the op-amp, such as input-referred voltage noise and current noise, can impact the signal-to-noise ratio of the TIA, especially for low-level input currents.
Stability Considerations
The inverting operational amplifier trans impedance amp can be susceptible to stability issues, particularly at high frequencies or with large values of R_f. To ensure stable operation, the following design considerations should be addressed:
Compensation Capacitor: Adding a compensation capacitor, C_c, in parallel with the feedback resistor, R_f, can help stabilize the TIA by introducing a dominant pole and improving the phase margin.
Bandwidth Limiting: Limiting the bandwidth of the TIA, either through the use of a low-pass filter or by selecting an op-amp with a lower GBW, can help improve the stability of the circuit.
Feedback Resistor Value: As mentioned earlier, the value of R_f can significantly impact the equivalent inductance of the input impedance, which can lead to stability issues. Careful selection of R_f is crucial for maintaining stable operation.
Parasitic Capacitances: Parasitic capacitances, such as those introduced by the op-amp, the feedback resistor, and the input wiring, can also affect the stability of the TIA. Minimizing these parasitic capacitances through proper layout and shielding techniques can help improve the circuit’s stability.
Applications of Inverting Operational Amplifier Trans Impedance Amp
The inverting operational amplifier trans impedance amp finds numerous applications in various fields, particularly in the realm of current-based sensor interfacing and signal conditioning.
Photodiode Amplifier
One of the most common applications of the TIA is as a photodiode amplifier. Photodiodes are current-based sensors that generate a current proportional to the incident light intensity. The TIA is an ideal choice for converting the photodiode’s current output into a voltage signal that can be further processed or measured.
Current Sensing
The TIA can also be used for general current sensing applications, where the input current is converted into a proportional voltage signal. This is useful in power management, motor control, and other systems where accurate current monitoring is required.
Electrochemical Sensor Interfaces
In the field of electrochemical sensing, the TIA is often employed to interface with current-based sensors, such as amperometric electrodes or ion-selective electrodes. The high input impedance of the TIA allows for accurate measurement of the small currents generated by these sensors.
Radiation Detection
In radiation detection systems, such as those used in medical imaging or nuclear instrumentation, the TIA is commonly used to amplify the current signals generated by radiation detectors, such as photodiodes or avalanche photodiodes (APDs).
Impedance Measurement
The unique input impedance characteristics of the TIA can be leveraged for impedance measurement applications. By monitoring the voltage output of the TIA, the input impedance of the circuit under test can be determined, which can be useful in various electrical and electronic characterization tasks.
Conclusion
The inverting operational amplifier trans impedance amplifier is a versatile and powerful circuit that plays a crucial role in a wide range of applications, particularly in the field of current-based sensor interfacing and signal conditioning. By understanding the technical details, design considerations, and practical applications of the TIA, electronics engineers and researchers can leverage this circuit to achieve accurate, stable, and efficient current-to-voltage conversion in their projects.
