Jawaharlal Nehru Technological University Hyderabad B.Tech III ANALOG COMMUNICATIONS Previous Question Paper (October - 2020 - R13)

A balanced modulator consists of two identical transistors connected in a differential amplifier configuration where the carrier signal is applied in push-pull mode to the bases and the modulating signal is applied in common mode to the emitters. The output is taken across the collectors.

The collector currents are given by i_c1 = I₀(1 + m(t))cos(ω_ct) and i_c2 = I₀(1 - m(t))cos(ω_ct). The output voltage v_o is proportional to the difference between these currents:

This expression represents the product of the message signal m(t) and the carrier signal cos(ω_ct), which is the definition of a DSB-SC wave, as the carrier frequency component is cancelled out due to the balanced structure.

In a synchronous detector, the received DSB-SC signal s(t) = A_mm(t)cos(ω_ct) is multiplied by a locally generated carrier cos((ω_c + Δω)t + φ), where Δω is the frequency error and φ is the phase error.

The multiplier output is:

Using trigonometric identities, this simplifies to:

After passing through a low-pass filter, the high-frequency term is removed, leaving:

The effects are as follows:

• Phase Error (φ): If Δω = 0, the output is (A_m/2)m(t)cos(φ). The amplitude of the recovered signal is scaled by cos(φ). If φ = 90°, the output becomes zero, resulting in quadrature null effect.
• Frequency Error (Δω): If Δω ≠ 0, the output is multiplied by a time-varying term cos(Δωt + φ). This causes the amplitude of the recovered message to fluctuate at the beat frequency Δω, leading to severe signal distortion.