pp 146-155
6.1 Introduction - Basic principles
O is an electronic oscillator circuit which generates an output signal without periodic signal is input to input. O harmonic oscillator, which is often called linear oscillator, is sub-electronic oscillators which generate the esodo the signal is approximately sinusoidal.
The oscillators are finding applications in many areas, including audio frequency systems and telecommunications. These systems use different oscillators including crystal oscillators and voltage controlled oscillator (VCO). Although there are a variety of integrated circuits to produce periodic signals, the oscillator with discrete components have significant advantages over into many integrated circuits. Thus, for example in many cases the oscillators integrated circuits can be designed at high frequencies and small noises, which are requirements of many telecommunication systems.
Similarly, the oscillators used in high-fidelity sound systems must have high stability and low noise and therefore designed with discrete components.
Basically, the harmonic oscillators are divided into two major categories are the resonant and non resonant oscillators. The syntonizamenoi harmonic oscillators consist of a lattice of coordination and an active LC component
(Transistor <TE), while non-resonant harmonic> vibrators consist of an active element and a
netting RC.
In current form, the oscillator is an amplifier with anasyzefxi (feedback) in which a portion of the output voltage returns to the entrance of a through truss anasyzefxis. If the signal is anasyzefxis appropriate width and phase, the circuit generates by itself (without the signal to the input) sine-wave tomorfi. The power required for this output signal is taken up by the voltage of the circuit.
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6.2 Criteria for oscillation
The Sch.v.iv shows the block diagram has a standard harmonic oscillator, considered like a special case of evolution and an amplifier anasyzefxi whose block diagram shown in Sch.6.1a.
point
(A) (b)
Figure 6.1. Jump from the block diagram anasyzefxi amplifier (a) oscillator
(B)
As observed, the system consists of a voltage amplifier (active element), with assistance If a lattice anasyzefxis reason to downgrade or anasyzefxis b and a summation point. The ac output voltage from the point summation denoted by ve and
the difference of the input signal minus the voltage v (output) of anasyzefxis vf (n - vf). The
relationships governing this block diagram are:
(6.2.1)
(6.2.2)
(6.2.3)
From these equations prove the following relationship:
(6.2.4)
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Afeinai where the (total) aid anasyzefxi <strengthening with closed loop, if it is the
aid without anasyzefxi and B if the support of the open loop.
From Eq. (6.2.4) that if b = 1 then if | Af | = | no/n1 | = ¥ | This means that the system will produce output n0 ^ 0 without being logged (n = 0), that will act as oscillator with a structural diagram of Sch.6.1 b
Therefore, the complex equation
If b = 1 (6.2.5)
condition called Barkhausen, is the condition we have to start from the system oscillations.
This equation, after appropriate mathematical treatment proved equivalent to the equations:
(6.2.6)
phi = 0 ° (<360 °) (6.2.7)
where, phi the phase difference ypeisagei the total open loop circuit (amplifier + anasyzefxis netting). The Eq. (6.2.6) and (6.2.7) give the following two conditions required for oscillation to have:
1. The measure of assistance open loop if b should be 1.
2. The total phase change through open loop should be 00 <360 °.
These two conditions are called oscillation criteria Barkhausen.
So if the amplifier generates phase transition Sch.6.1 1800 then we have to swing the panel must create anasyzefxis 1800 other phase difference so that the total phase change of the open loop system is 3600 (or 00).
Note that the waveforms showing the sine and Sch.6.1 is used to show only the action of the circuit. In the general case, the waveform generated by an oscillator depends on the circuit elements and therefore can be sine, square or triangular.
Moreover, the frequency of oscillation is basically determined by the lattice data anasyzefxis.
Harmonic TALANTOTES
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6.2.1 Starting and Maintenance of oscillations
The criteria Barkhausen, either expressed Complex with the general Eq. (6.2.5) or the individual Eq. (6.2.6) (meter) and Eq. (6.2.7) (phase) are mathematical equations - conditions of critical values which provide just the start (the start of oscillations). In practice, fast, these conditions tend to be reversed, either because the values of the circuit (R, L, C, etc.) change due to the passage of the current operation of the resulting heating of the circuit, either because parameters of active components (transistors, etc.) vary for the same reasons. Thus, the second and especially the Ln amplifier no longer meet the condition and the Barkhausen oscillation tends to be redeemed shall cease to be. To circumvent this problem, and ensure a dependent oscillations, forced to give the amplifier circuit gain value slightly larger AO than is required by Eq. (6.2.5). So, to have oscillations dependent must meet the Barkhausen condition but not as equal as inequality of the form
(6.2.8)
when the criteria Barkhausen, are
| A b |> 1 (6.2.9)
and
phi = 0 ° (6.2.10)
It turns out that where the above, the amplifier maintains the oscillations not only by providing reinforcement, and the corresponding power supply, but, and mediated by a phenomenon called the width restriction. This phenomenon, which is because the voltage gain of the amplifier AO decreases with increasing the amplitude leads to maintenance of constant width.
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6.3 Resonant oscillators
Its coordinating oscillators and oscillators called LC,
why are anasyzefxis netting a resonant circuit L-C (often combined with resistance R). The oscillators are used especially in radio applications with frequencies ranging from several hundred kHz to several hundred MHz. The most common of this type oscillators are oscillators Colpitis, Clapp and Hartley which will see further below.
The basic structure of the LC oscillator shown in the block diagram of Sch.6.2.
As shown consists of a voltage amplifier AO and a lattice anasyzefxis the general case that includes three circuit elements 1, 2, 3 (with L and C) with a medium receive between 1 and 2. These elements constitute a general resonant circuit. With the help of the Barkhausen criteria is shown that to have a dependent oscillations oscillators with them, must apply to relations:
X1 + X2 + X3 = 0
Figure 6.2. Basic structure oscillator LC (coordinated)
Similarly, by Eq. (6.3.2) we find that to be dependent oscillations we must apply
| If |> 1 + C (6.3.5)
C1
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151
where X1, X2 and X3 are apparent resistances, with Xk =] oh Lk for cleaning
Res reactors (inductors) and Xk = 1 /] h Ck for net capacities
(Capacitors).
6.3.1 Oscillator Colpitis
Feature an oscillator Colpitis is that as soon
nizomeno circuit consists of two capacitors, C1, C2, in series
and their system parallel to the inductor L. The two capacitors
create an ac voltage divider, and the trend is anasyzefxis vf
that develops at the ends of C2 (middle receive between
C1 C2) and led to the amplifier gain A.
In the above, and referring to an oscillator Sch.6.2
Colpitts we have X1 =, X2 =] oh C2, and X3 =] oh L. From the relations
these and Eq. (6.3.1) show the relationship
(6.3.3)
where, Ct equivalent capacity of the connection of C1 and C2 in series, ie
(6.3.4)
The Sch.6.3 depicting Colpitts oscillator transistor (BJT) in connection CB. The positive anasyzefxi the extreme to take the middle between the C1, C2, leading to the entrance of the transistor. The emitter resistance Re is inserted which, together with the R and R2, create the polarization of the transistor. At the same time, it carries negative anasyzefxi function, to improve-ment sine waveform generated by the oscillator. Finally, the RC is the classical resistance of the transistor collector.
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Figure 6.3. Colpitts oscillator with a BJT
Considering the expression of the gain of the amplifier in Lo
function of the transistor hybrid parameters, Eq. (6.3.5) becomes:
where
Ri = h + (1 + h,) R
(6.3.6)
(6.3.7)
Example 6-1
The above oscillator with a BJT Colpitis implemented with the following component values: L = 100, C1 = 1 nF, C2 = 100 pF, Rc = 680 O, R1 = 18 kO, R2 = 5.6 kQ, Re = 47 W. Furthermore, the transistor has hie = 1 kQ and hfe = 199. To find the oscillation frequency and to determine whether the oscillations are maintained.
Solution
From Eq. (6.3.4) we have
1 = 71 +71 1 9 = 109 + 1010 = 1.1x 1010 L
Ct C1 C2 10-9 0.1 X10-9
1
O Ct =! - = 91 pF
t 1.1 x1010 H
Besides, from Eq. (6.3.7) we have
R. = H. + (1
ie x
Thus, Eq. (6.3.6) gives
APMONIKOI TALLNTOTES 153
Therefore, from Eq. (6.3.4) we have
whenever
Therefore satisfied the inequality of Eq. (6.3.6), so we
maintenance of oscillations.
The circuit Sch.6.4 depicting Colpitts oscillator with TE. O TE
gives the necessary support to have maintenance of oscillations. The oscillation frequency is still given by Eq. (6.3.3).
Also, we have to maintain the oscillations should again be
anisotiki apply Eq. (6.3.5)
Finally, as seen from the figure, the coefficient anasyzefxis
b (X2 / (X1 + X2)) is given by:
P = CTC; <6 • 38)
(This is taken into account that the input impedance of the TE is very
large).
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Figure 6.4. Colpitts oscillator with TE
Example 6-2
We compute Colpitts oscillator with TE frequency 50 kHz, money-
simopoiontas the 741 (Ri = 2 MO, R0 = 70 Z).
Solution
We start assuming the coil a reasonable value, eg L = 1 mH, so
Eq. (6.3.3) gives
C = 1 = 1 = 1 = 10 1 nF
1 (2p/0fL 4chp x/0x L 4x p 2 x 502 x 106 x 10-3 '
We therefore anasyzefxis a standard price,
Therefore, this is associated
C1 - 1, C2
Assuming a reasonable value for C2 = 10 nF, calculate the C1
C1 = ^ ^ C2 = T ^ 1nF 1.1 nF
XC1 =
Therefore,
R1 = 10XC1 = 10 x 289 = 2.89 k0 Z
We accept R1 = 10 KO and calculate R2 from the known formula
gain of the amplifier with TE reversed
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155
To accept a value R1 R1> XC1 that the panel not to load the amplifier.
In practice we get,
R = 10 ha
(6.3.9)
where,
(6.3.10)
Therefore,
The resistor R2 in practice is usually a potentiometer to adjust around
above the price that we have good sines Nikos signal at the output of
oscillator.
