FM Balanced Slope Detector

A balanced slope detector is an improved version of the slope detector. The drawback of harmonic distortion is removed in this detector by using two slope detectors instead of one as in a single-tuned slope detector.

Circuit Description

The circuit diagram, shown in Figure (a), has two slope detectors marked slope detector 1 and slope detector 2. Both the slope detractors are called balanced because they have identical components as follows:

• Slope detector 1: It consists of a detector diode D₁, filter capacitor C₁, load resistor R₁, and variable capacitor C_T1. The variable capacitor C_T1 is called the tuning capacitor because it is adjusted to tune the upper winding of the secondary Winding of the input transformer T.

• Slope detector 2: It consists of a detector diode D₂, that is identical to D₁. It also has filter capacitor C₂, load resistor R₂, and variable capacitor C_T2. The tuning capacitor C_T2 tunes the lower winding of the secondary winding of the input transformer T.

The two slope detectors are balanced because C₁ = C₂, R₁ = R₂, and D₁ is identical to D₂. The upper and lower windings of the secondary windings of the center-tap transformer T are also identical.

The primary winding of the input transformer T is tuned to the central frequency of the carrier signal f_c by using the tuning. capacitor C_T. The secondary windings are tuned to different frequencies so that the circuit is staggered tuned. The outputs of the detector diodes D₁ and D₂, are filtered by C₁, R₁ and C₂, R₂, respectively. The voltage V₁. which is developed across R₁, and voltage V₂, which is developed across R₂ are added together between the points E and F to get the final output voltage V_o, which is the modulating voltage e_m.

Circuit Operation

The operation of the circuit can be explained by considering the two slope detectors separately.

Slope Detectorn 1

The resonating frequency of slope detector 1 is set to f₁, by adjusting C_T1 so that it is greater than f_c by an amount of ∆f. As a result, slope detector 1 is tuned to f_c, given as:

f₁ = f_c + ∆f

The signal coupled to the upper winding of the secondary winding of the transformer T has a central frequency f_c. If the maximum frequency deviation of the incoming FM signal, r(t), is ±f_d, the operating range of slope detector 1 is between f_c and (f_c + f_d), shown in figure (b). Which illustrates the frequency response curve of both slope detectors.

When the incomning signal frequency deviation between f_c and (f_c + f_d), diode D₁ is forward biased becouse voltage V_D1 increases according to the frequency response response curve of slope detector 1. The diode rectifies this amplitude and frequency modulated signal. Capacitors C₁ and resistor R₁ then filter the rectified voltage. The voltage so developed across R₁ is the positive half of the modulating signal. This can explained by the frequency-deviation curve applied at f_con the frequency-axis of Figure (b). The positive half of the frequency-deviation curve lies in the response curve of slope detector 1. Therefore, the frequency deviations that are greater than are converted into coresponding amplitude by slope detector 1.

Slope Detector 2

Slope detector 2 is tuned to f₂, by adjusting the tuning capacitor C₂ such that:

f₂ = f_c - ∆f

The input FM signal whose frequency deviation lies between f_c and (f_c — df) is converted into corresponding amplitude variations by slope detector 2 because this part of the frequency-deviation curve lies toward the frequency-response curve of slope detector 2. The voltage V_D2, developed across the lower winding of the secondary winding of the transformer T is amplitude-and frequency-modulated, which corresponds to the frequency deviation from f_c to (f_c — df). This voltage, V_D2 is rectified by diode D₂, because it is forward-biased and the capacitor C₂, filters this rectified voltage. The filtered voltage is developed across R₂ and, as a result, the output of the balanced slope detector is the negative half of the modulating signal corresponding to the frequency deviations lower than f_c.

Combined Response of Slope Detectors 1 and 2

The output of the balanced slope detector is the combined output of the individual slope detectors. Slope detector 1 provides the positive half of the modulating signal across the Output terminals E and F. When D₁ is forward-biased, the diode D, is also slightly forward-biased because the voltage developed across the lower winding is very small. This is because slope detector 2 is tuned to (f_c — ∆f), while the incoming signal lies between f_c and (f_c + ∆f)

The conduction of diode D₂, results in a small current that flows though R₂ from F to D. The direction of the current due to D₁ is from E to D through R₁

Therefore, when a positive voltage is developed across R₁ a very small negative voltage also develops across R₂. The sum of these two voltages appears between output terminals E and F.

Thus, the final output is sligtly reduced by a negative voltage developed across R₂, because: -

V_o = V₁ - V₂

A similar action takes place when the incoming FM signal contains the frequency deviations between f_c and (f_c - df). The diode D₂ is forward-biased because appreciable positive voltage V_D2 appears across D₂. This is because slope detector 2 is tuned towards (f_c - df). This frequency-deviation range lies in the negative half of the modulating signal. As a result, the voltage developed across R₂ after filtering the rectified output of D₂ is the negative half of the modulating signal.

During the conduction of D₂, a small voltage also appears across the upper winding of the secondary winding of transformer T. This voltage is small because the upper winding is tuned to (f_c — ∆f), while the incoming voltage lies in the frequency range f_c to (f_c — ∆f). Due to this voltage, diode D₂, also supplies a positive voltage across R₁. This positive voltage slightly reduces the negative voltage appearing across R₂, when summed up between the output terminals E and F. The net voltage is still a negative half cycle of the modulating signal.

The positive and negative halves of he modulating signal are available across the output terminals of the balanced slope detector marked as shown in Figure (b). The overall response of both slope detectors is shown in Figure (b), and the operating range at the curve is marked between the points K and L. This operating range of the overall response curve is a straight line, and therefore, the operation is linear. This removes the; nonlinear behavior of a single-tuned slope detector, and the higher harmonics are not generated in a balanced slope detector.

The overall response curve takes the shape of the letter S, as shown in the Figure (b). This is called S-response of the FM detectors.

Drawbacks of Balanced Slope Detector

Although a balanced slope detector is better than a slope detector. it has following drawbacks:

• The detector has three windings in the input transformer T, and all of them are tuned to different frequencies. The primary winding is tuned to tha central frequency of the carrier, f_c, using the tuning capacitor C_T. The two secondary windings are tuned to (f_c + ∆f) and (f_c — ∆f) using the tuning capacitors C_T1 and C_T2. The alignment of three tuned circuits, called staggered-tuned, is a difficult task that should be accomplished with accuracy to obtain a linear S-curve.
• This slope detector also responds to the amplitude variations of the input Therefore, it may not provide a true modulating signal.
• The operating frequency range is increased after obtaining an S-shape, but its performance does not improve.