In today's tutorial on Aggregation Amplifiers, the voltages or signals applied to multiple inputs of an inverted transactional amplifier circuit can be "collected" together to produce a single output, and depending on the amplifier configuration, the output signal will be the positive or negative sum of all inputs, whether inverted or not.
We also found that the aggregation amplifier multiplied each input voltage by its weighted gain, which is determined by the Rε/RIN ratio, that is, the ratio of feedback resistance (Rε) to the corresponding input resistance (RIN).
The collected output voltage (or signal) can be the result of a direct insertion method in which each input resistance (RIN(1) to RIN(n)) has the same values and produces a linear output voltage corresponding to these values, or it can be the result of a binary-weighted method in which the value of each input resistance produces a gradual output voltage corresponding to the "weight" of each input value. It has many electronic applications such as aggregation amplifiers, audio mixer designs or analog-to-digital conversion (ADC), etc.
However, in addition to using transactional amplifiers as aggregation amplifiers (aggregation) or differential amplifiers (subtraction), we can also configure a large number of input transactional amplifier circuits that will function as an Average circuit that can produce an output voltage corresponding to the average voltage value. two or more entries.
Passive Average Value is a basically resistant network or circuit structured to provide an output voltage whose value is equal to the mathematical average of all input voltages. Any number of inputs can be used to create a passive or active average circuit. Consider the following 2-input resistant circuit.
Here the two resistors, R1 and R2, are connected so that one end of each resistance creates a common connection or node, while a voltage source is applied to the other end of each resistance, as shown.
This then forms the basis of a passive average circuit that produces an output voltage equal to the average value of the two input voltages, as they are effectively connected to each other through resistors. This basic circuit configuration can also be used for collection and subtraction circuits.
Kirchhoff's current law (KCL) states that the algebraic sum of all electrical currents entering and exiting a circuit connection or node must be equal to zero. Thus, the sum of the currents passing through this passive resistant circuit will be equal to: IT = IR1 + IR2.
This basically means that since resistors are effectively connected in parallel with each other through voltage sources, the sum of VOUT's input currents is equal to the division of separate resistors into mutual value, and this idea forms part of the Millman Theorem. This is V = I/G, where "G" is conductivity. Then we can expand this basic 2-input passive average equation for resistant circuits with multiple resistance and voltage inputs of more than 3, 4 or more, as shown.
Centerer Amplifier Equation
Therefore, any number of inputs can be used to produce a passive average circuit with the voltage seen on the common node, the mathematical average of all input voltages.
Centerer Amplifier Example
A passive average circuit with 2 inputs is created using interconnected resistance of 2kΩ and 4kΩ. If there's a voltage supply of 12 volts d.c. It is connected to one end of the 2kΩ resistance and a second 6 volt d.c voltage source. 4kΩ is connected to one end of the resistance. Calculate the output voltage on the common connection.
First, assume: R1 = 2kΩ, R2 = 4kΩ, V1 = 12V and V2 = 6V.
Thus, the common node connection voltage is calculated as 10 volts. But you may be sitting there thinking: (12 + 6)/2 = 9 volts. The average voltage output should be 9 volts, and you are right. However, the two resistors used in this example have different values, 2kΩ and 4kΩ, so it will affect the currents flowing from the resistant network that produces what is known as the Weighted Average Circuit. This means that each input is multiplied by the weight factor before it is averaged.
In fact, for this simple example, IR1 will be the one that flows into the connection (12-10)/2000 = +1mA and the IR2: (6-10)/4000 = -1mA that flows out of the connection. This flows 1mA current from the larger 12-volt feed to the smaller 6-volt feed via the common connection.
However, if we make these two input resistances equal to R1 = R2 = R, the current flowing from the connection will be zero because the two IR1 and IR2 currents are the same but opposite value, so cancel. Then the above passive average equation is also simplistic:
Passive Average Equation
That is, with equal resistance values instead of different individual resistance values, the output voltage value in the common connection will be exactly equal to the average value of separate voltage sources, making it a real passive average circuit. Then, using our simple 2-input average circuit above, we expect VOUT = (V1 + V2)/2 = (12 + 6)/2 = 9 volts.
Op-amp Average Circuit
One main drawback of the above passive average circuit is that the output voltage can be affected by a connected load, especially if the load is low impedance. However, we can ensure that the average output voltage of the Centerer Amplifier circuit remains accurate and constant by adding a transactional amplifier to its output, converting it into an active average circuit.
The simplest and easiest way to do this is to connect the output of the resistant average network to a transactional amplifier or "op-amp" input configured as a non-inverted "voltage tracker". A voltage tracker is basically a union gain buffer that produces a positive output voltage, as shown.
Centerer Amplifier Circuit Using Voltage Tracker
As we have seen in previous lessons, the input impedance of an op-amp is extremely high, so the current does not flow into the inverted input terminal. Since the op-amp output is directly dependent on the inverting input, the feedback will therefore be 100%, so the VIN is exactly equal to VOUT, giving the op-amp a fixed "1" or union gain.
This VOUT = VIN produces a positive output average circuit. The advantage here is that individual inputs are effectively ins isolated from each other and therefore from any connected load, so that any number of entries can be used.
We can also configure the transactional amplifier as an inverter to produce negative output average voltage. Closed loop voltage gain (AV(CL)) resulting from the feedback path between the output and input terminals is given as follows:
AV(CL) = -Rε / RIN = VOUT / VIN
Then we can rewrite it as follows:
But for our average riser, vin = V1 + V2 + V3 + … + etc. If we use an average circuit with 3 inputs for simplicity, the expression of the output voltage will be as follows:
Thus, each input voltage is multiplied by a common -Rε/RIN factor. If we make all resistance values equal and the same, this feedback resistance is Rε = RIN = "R" and the number of entries is 3. Then Rε = RIN1 = RIN2 = RIN3 = R and "n" = 3, then the equation above becomes:
Setting the closed-loop voltage gain of the transactional amplifier equal to the reciprocal value of the number of inputs of 3 in this given example will reverse the output voltage from the op-amp average circuit (-VOUT) and the mathematical average value of three separate inputs, as shown.