MAXWELL BRIDGE:

• For frequencies much below 1MHz RC oscillators become more practical than LC types because of the physical size and expense of the inductors and capacitors required at low frequencies. A problem arises with RC oscillators however, when a variable frequency is required.
• In LC oscillators a single tuned circuit controls the frequency, which can be changed simply by making either a single inductor or a single capacitor variable.
• The frequency of oscillation in RC types, such as the phase shift oscillator, is controlled using multiple RC combinations to produce the correct amount of phase shift at the required frequency.
• To alter the frequency, it is therefore necessary to alter the value of at least three components, either resistors or capacitors simultaneously.
• Even though it is possible to manufacture ganged variable capacitors, the size of capacitors needed at low (e.g. audio) frequencies means that the capacitors would have to be physically too large to be practicable.
• It is also possible to manufacture multiple variable resistors but much more difficult to ensure that the tracking of such components is accurate enough, i.e. as the resistance of the multiple resistors is varied, they must each change their resistance at exactly the same rate.
• Again the cost of suitable components becomes impractical for many purposes.
• In addition, it is possible to build Wien Bridge oscillators having very low levels of distortion compared with Phase Shift designs.

OPERATION OF MAXWELL OSCILLATOR:

• The circuit is set in oscillation by any random change in base current of transistor Q1, that may be due to noise inherent in the transistor or variation in voltage of dc supply.
• This variation in base current is amplified in collector circuit of transistor Q1 but with a phase-shift of 180°. the output of transistor Q1 is fed to the base of second transistor Q2 through capacitor C4.
• Now a still further amplified and twice phase-reversed signal appears at the collector of the transistor Q2.
• Having been inverted twice, the output signal will be in phase with the signal input to the base of transistor Q1 A part of the output signal at transistor Q2 is fedback to the input points of the bridge circuit (point A-C).
• A part of this feedback signal is applied to emitter resistor R4 where it produces degenerative effect (or negative feedback).
• Similarly, a part of the feedback signal is applied across the base-bias resistor R2 where it produces regenerative effect (or positive feedback).
• At the rated frequency, effect of regeneration is made slightly more than that of degeneration so as to obtain sustained os­cillations.
• The continuous frequency variation in this oscillator can be had by varying the two capacitors C1 and C2 simultaneously.
• These capacitors are variable air-gang capacitors. We can change the frequency range of the oscillator by switching into the circuit different values of resistors R1 and R2.
• The advantages and disadvantages of Wien bridge oscillators are given below:

ADVANTAGES:

• Provides a stable low distortion sinusoidal output over a wide range of frequency.
• The frequency range can be selected simply by using decade resistance boxes.
• The frequency of oscillation can be easily varied by varying capacitances C1 and C2simultaneously.
• The overall gain is high because of two transistors.

LIMITATIONS OF MAXWELL BRIDGE:

• The circuit needs two transistors and a large number of other com­ponents.
• The maximum frequency output is limited because of amplitude and the phase-shift characteristics of amplifier.

DERIVATION FOR UNKNOWN INDUCTANCE AND CAPACITANCE:

• In this bridge the arms bc and cd are purely resistive while the phase balance depends on the arms ab and ad.
• Here l1 = unknown inductor of r1. l2 = variable inductor of resistance R2. r2 = variable electrical resistance.
• When Potential between two arms are same as the opposite arm we get the balance condition
• Hence we have

$L_1=\dfrac{r3}{r4}l2$ and

$r1=\dfrac{r3}{r4}(r2+R2)$

• In this Maxwell Bridge, the unknown inductor is measured by the standard variable capacitor.
• Here, l1 is unknown inductance, C4 is standard capacitor. Now under balance conditions we have from ac bridge that

$Z_1Z_4=Z_2Z_3$

That is

$r_1+j\omega L\dfrac{r_4}{1+j\omega C_4R_4}=r_2.r_3$and

$r_1.r_4+j\omega L_1.r_4=r_2.r_3+j\omega r_2.r_3.C_4.r_4$

Here C1 is the capacitance and L1 the inductance

Let us separate the real and imaginary parts, the we have,

$C_1=r_2.\dfrac{r_3}{r_4}$ and $L_1=r_2.r_3.C_4$