ECE 3336 Introduction to Circuits & Electronics General: Electronics Specific: Amplifiers Fall 2007, TUE&TH 4:00 -5:30 pm Dr. Wanda Wosik Electronics Distinction between Electrical Circuits and Electronics is somewhat artificial but quite well established.
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TUE&TH 4:00 -5:30 pm
Dr. Wanda Wosik
We can only see amplification of amplitudes or power if we balance the energy of the system. For that we have to use power supply to “empower” the amplifiers. Therefore, we have to use voltage sources.
Amplifiers use DC power supply that enables them to operate.
With this notation, the total voltage that has both the dc and ac components can be written: vA = VA + va.
There are various gains that we need to describe amplifiers
Voltage gain in dB is 20(log10|Av|).
Voltage gain Av is the ratio of the voltage at the output to the voltage at the input.
Current gain Ai is the ratio of the current at the output to the current at the input.
Current gain in dB is 20(log10|Ai|).
Power gain Ap is the ratio of the power at the output to the power at the input.
Power gain in dB is 10(log10|Ap|).
We will focus on operational amplifiers, specifically on
Voltage at the output is obtainedwith respect to a reference (ground). That creates a single ended output.
The differential input indicates a voltage difference applied between the input terminals. These inputs are called inverting and noninverting
Operation of op-amps requires power supply. So there are symmetrical dc voltage sources that are used in op-amps (frequently ±15V). Op-amps are made as ICs. Pins contacting various nodes (inputs, output, supply voltages etc.) are shown below.
Positive dc power supply
Bipolar transistors are used for building an op-amp
There are other op-amp designs where MOS transistors are used.
Negative dc power supply
Equivalent circuit of the op amp includes
Equivalent Circuit for the Op Amp
The output voltage should be ZERO volts for v-= v+ i.e. vin=0V.
This is called common mode rejectioni.e. common or the same voltages will not be amplified despite a very large voltage gain AV(OL) in the open loop (OL) op-amp..
But op-amps are not perfectly symmetrical and some signal at the output may appear. We will talk (later) about the common mode rejection ratio to describe this effect.
Equivalent Circuit for the Op Amp
The maximum positive value of the output voltage is limited by thepositivedc power supply voltage(V+) and the minimum voltage is limited by the negativedc power supply (V-). This restrictions impose limits on the input voltage, which for the open look configuration, cannot be small enough to avoidsaturation. We will always see saturation in the open loop configuration.
There are two assumptions important while analyzing and designing op amp circuits. We will call them golden rules and we will use them always whenever the op amps can be treated as ideal elements.
The first assumption:
i- = i+ = 0
results from large resistances at the input. Currents do not flow into the op-amp.
The second assumption:
deals with the output that makes the input voltages equal v+≈v-. This is realized by introducing a negative feedback loop, which will span the output and the inverting input.
negative feedback loop
The second golden rule v- = v+results in the virtual short, or the summing-point constraint. The constrain refers to the input voltages, which become the same if there is a negative feedback and the open loop gain Av(OL) is large.
Without negative feedback, even a small input voltage will cause saturation of the output either at V+ or V-.
NO NEGATIVE FEEDBACK yet
This is open loop configuration
+ dc V supply
Engineers have developed a way of looking at signals called the signal flow diagram. This is not a schematic, and does not represent wire and specific components. A line represents a path that a signal might follow. The signals can be voltages or currents. Therefore, we will label the signals with the symbol x.
In the signal flow diagram shown below, there is an input signal, xi. This signal flows into an amplifier with gain A, which is shown with a triangle. This produces an output signal xo. The input is multiplied by the gain, to give the output.
Signal Flow Diagram
Feedback notes were developed by Dr. Shattuck
Now, let’s add negative feedback to our signal flow diagram. In the signal flow diagram shown below, we add another amplifier. This amplifier has a gain which is conventionally called b. This amplifier amplifies the output signal, to produce a feedback signal, xf. Finally, this feedback signal is subtracted from the input signal. The symbol for this action is called a summing point or a summing junction. The signs at the junction indicate the signs for the summation.
subtracted from the input signal
At this point, we can define negative feedback. Negative feedback is when a portion of the output is taken, returned to the input, and subtracted from this input.
If we were to add it to the input, we would call it positive feedback.
The feedback amplifier, with a gain of b, is typically not an amplifier per se, but rather is a passive (resistive) network. The key is that the feedback signal xf is proportional to the output signal, with a multiplier equal to b.
The gain A is called the open loop gain (our AV(OL)), because this would be the gain if the loop were to be opened, that is, if the feedback were removed.
The input signal, which includes -ve feedback gain
Now, let’s solve for the gain with negative feedback, which is xo/xs. We start by writing an equation for the summing junction, taking into account the signs, to get
Next, we use a similar definition for the feed-forward gain, A, to write
We then substitute the first equation into the second to get
We can combine terms, then we can divide through by xs, and then by (1+Ab), to get
This is the gain with negative feedback (a closed loop gain)
If we take the case where A is very large, and it usually is, we can get a special situation. Specifically, take the case where Ab >> 1. Then,
and we can use this approximation to simplify the gain with feedback, which we call Af, to
Thus, the gain with negative feedback, Af, is
The onlyrequirement is that Ab >> 1. Thus, the gain is not a function of A at all !?!This is a seemingly bizarre, but wondrous result, which is fundamental to the power of negative feedback.
The gain of the op amp, which changes from time to time, and from op amp to op amp, does not affect the overall gain with feedback.
Important, so it is repeated again: The gain with negative feedback, Af, is
With this result, we can look again at the signal flow diagram. The input to the op amp, vi, is the outputdivided by the gain, vo/A. If A is large, then viwill be much less than vo, and can usually be neglected. Neglect the input?No -neglect the differential signal at the input vi!
So we have our second golden rule v+=v-
Thus, the gain with negative feedback, Af, is
This is what we call the virtual short.
In op-amps we also can have a feedback loop that would span an output and the noninverting input. This will be called Positive feedback, which is also very useful for some applications. However, we will stay with negative feedback loops in our circuits. Always verify that there is a loop like that in your circuit.
Negative feedback adds a portion of the output signal to the inverting input. Since the signs of these voltages are opposite, the negative feedback acts as if the signal applied to the input decreases.
The net result is that the output voltage can be controlled by the external elements and does not saturate.
If assumptions that the op-amp is ideal (most of the times) are true we will apply two golden rules to solve circuits
1)i- = i+ = 0.
2) v- = v+. Virtual short
An op amp operates in the inverting configuration when the input voltage is applied to the inverting terminal.
RF is the feedback resistor
Rs is the source resistor
There is a negative feedback loop on RF
That assures that we have the virtual short:v-=v+. Since v+=0V also v-=0V.
The op-amp does not draw currents iin=0A
To find vout we have to find vRF.
To find vRF we have to know current iF which can be calculated from is.
The current is is given by the voltage Vs and Rs.
If we have golden rules (iin=0, v+=v-)
Closed loop voltage GAIN:
The negative feedback loop, combined with the ideal properties of the op-amp (high open loop gain 105-107 and large input resistance) ensures that
n=1, 2, …, N
The virtual short results in virtual ground at the inverting input.
The voltage at the output is inverted in phase and includes voltage sources weighted by a ratio of resistors