Effect of feedback on frequency response
pp 40-48
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2.5 Effect of feedback on frequency response.
We have seen so far that the negative feedback amplifier alters the gain (voltage and current) and the input and output resistances. Besides these, it turns out that the negative feedback and alter the frequency response of the amplifier.
The study is then generally refers to the frequency response without discrimination. So when it comes to power amplifiers with feedback, we refer to the response stream.
When it comes to voltage feedback amplifiers, refer to the voltage response.
To find that changing the frequency response of an amplifier due to negative feedback, we consider the two basic frequencies that characterize the circuit of the amplifier without feedback. These two basic frequencies are respectively the lower cutoff frequency f1 and upper cutoff frequency f2. These frequencies are determined by the response curve of the amplifier gain, corresponding to 3 dB less than the maximum gain (or maximum gain of 0.707), as shown in Sch.2.8.
Figure 2.8. Effect of negative feedback in the frequency-response
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It turns out that these cutoff frequencies, with feedback and without feedback, connected by the equations:
(2.5.1)
(2.5.2)
For simplicity in notation, we omit the indices i and n the parameters b and A, where it is understood that they offer the indicators according to feedback ananaferomaste the current or voltage.
From Eq. (2.5.1) and (2.5.2) we conclude that: Negative anasyxefxi bring down the lower cutoff frequency f1 and brings about an increase of the upper cutoff frequency f2, namely:
provided that | A | >> 1
As crossing bandwidth, BW, an amplifier is defined as the difference of the frequencies f1 and f2 (corresponding to a gain of 3 dB below the maximum gain). That is,
BW = f2-f1 ~ = f2 (2.5.3)
because, f2 >> f1
When the amplifier has feedback, crossing the range given by such a relationship,
namely:
BWf = f2f - f1f ~ = f2f (2.5.4)
because, f2f >> f1f
From Eq. (2.5.3) and (2.5.1) shows:
BWf = BW (1 + b * A) (2.5.5)
This equation connects the width of the pass band frequency of an amplifier that works with feedback, with the width of the pass band frequency of the same amplifier when operated without feedback. From this equation we observe that when the amplifier
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working with negative feedback bandwidth crossing frequency is increased by the factor (1 + b * A). Thus, when | b * A | >> 1, the
increase would be significant.
Example 2-3
Work without an amplifier and a feedback voltage gain
If it = 1000. To gain by 3 dB below the maximum, the cutoff frequencies are f1 = 100 Hz and f2 = 100 KHz. The amplifier is converted to a feedback amplifier with negative feedback with a gain of 20dB.
To calculate the frequency response of the amplifier with feedback.
Solution
The frequency-response curve shown in Sch.2.8. From the
Our data, to gain feedback, we have:
20log (1 + b * Av) = 20
So:
1 + b * Av = 10
Therefore, the gain of the amplifier with feedback Avf will be:
If you want to convert this value into the Avf dB, use the following formula:
The two cutoff frequencies with feedback will be:
So, the bandwidth frequency transit
feedback will be:
Feedback circuit
Figure 2.9. Block diagram with feedback amplifier series
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Observe that the crossing frequency range, BWf, with feedback increased by 10 times compared with BW range without feedback.
It is worth noting that the same factor (ie 10) reduced the gain of the amplifier with feedback, compared to the gain without feedback. The above
analysis appears in Sch.2.8.
Feedback amplifier with 2.6 series
The Sch.2.9 shows the block diagram of an amplifier with feedback series. The series feedback amplifier with active diagogimotita alter the amplifier without feedback, according to the equation:
where: Gmf and Gm is the transconductance corresponding series with feedback and without feedback. Recall that diagogimotita is the inverse of resistivity, measured in S (Zimens) or mS (or mho or mmho).
O feedback coefficient is defined by:
Feedback amplifier
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Where Vf and virus symbolize respectively the feedback voltage range and output current. The vm has dimensions of resistance and is measured in ohms
Generally, the feedback amplifier range, the output current and allowed to congregate in the back entrance of the amplifier since converted to a voltage by means of the feedback resistor R. For this reason, the connection is called a voltage feedback amplifier - series.
In Sch.2.10 shows the equivalent circuit Sch.2.9.
Figure 2.10. Equivalent circuit of Figure 2.9.
Upon completion of the study for most types of feedback of an amplifier, we present the summary Table App 2.1. O This table helps us to compare the different parameters for different types of feedback.
2.7 Parallel Amplifier feedback branch
The Sch.2.11 block diagram showing the feedback amplifier with parallel branching.
The output voltage of the congregates the feedback circuit and returns to the input current form.
(2.7.1)
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Feedback amplifier
RL I
Figure 2.11. Structural diagram of negative feedback amplifier with parallel branching
We can design the amplifier with feedback that parallel branch in the form of a diantistasis amplifier as shown in Sch.2.12.
Figure 2.12. Equivalent circuit of the amplifier Sch.2.12.
U
O diantistasi term expressing the ratio of the output voltage V0 to the input current I?
denotes the internal resistance and through the aid ¬ schyti. The diantistasi equals
the inverse of the transconductance and is measured in ohms
If the feedback amplifier works with parallel branching, the
diantistasi of Rmf, given by the following relationship:
where Rm is the diantistasi the amplifier without feedback.
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O branching ratio BR parallel feedback is defined by:
(2.7.2)
O rate is measured in S <mS.
2.8 Improvement of deformation
Negative feedback in amplifiers resulting in the reduction of distortion due to nonlinearity. Specifically, feedback helps to reduce the width of distortive components generated signal.
If denote by Df and D on the back of deforming Con ¬ feedback signals with and without feedback, then the relationship that links them is the following:
where b and L refer to feedback voltage. Because 1 + cf> 1, it follows that Df <D.
So, the feedback demoted all the components of deformation.
Generally, each amplifier with feedback, because part of the output signal returns to the input of the amplifier, the output signal amplitude is less than would exist without feedback. As a result, the strain components and the noise generated in the circuitry of the amplifier is reduced to the width when the amplifier works with feedback. This also reveals
Eq. (2.8.1).
For> \ Rm >> (Ro + Ri) + For As >> 1 - RR ^ -
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COMPARATIVE TABLE FEEDBACKS
Table App 2.1
Equations with various types of amplifier feedback.
