Analog Communication Lab (EC39001)

Name: A Sai Rama Karthikeya

Roll No: 23EC10009
Experiment No: 2
Experiment Name: Switching Modulator Circuit
Group No: 27
Date of Submission: 12/08/2025
August 12, 2025

1 Introduction
A switching modulator uses a high-speed electronic switch (typically a JFET transistor) to impose a
carrier waveform on a message signal. The transistor is driven by a square-wave carrier: when the carrier
is high, the JFET turns OFF, allowing the message signal to pass through; when the carrier is low, the
JFET turns ON, shorting the message signal to ground and blocking it. This switching action effectively
modulates the message signal with the carrier frequency.
The switching action generates a train of message-shaped pulses. Passing this through a tuned band-pass
filter removes unwanted harmonics and retains only the carrier-band component, producing the desired AM
signal. This method of modulation is simpler than an analog multiplier and is power-efficient, although it
requires a high-speed switch and careful filtering to remove the harmonics.

2 Key Objectives
• Build and test a switching modulator circuit
• Design and calculate filter values
• Observe waveforms
• Understand switching modulation

3 Components Used
• Function Generator
• Mixed Signal Oscilloscope
• Breadboard and Connecting Wires
• JFET
• Resistors
• Capacitors
• LM741 Op Amp
• DC Power Supply

1
4 Theory
4.1 Switching Modulation
In a switching modulator, the transistor acts as an ideal on/off gate controlled by the carrier. When the
carrier drives the transistor base high, the transistor saturates and the message signal (applied to its input)
is conducted to the output. When the carrier drives the base low, the transistor cuts off and the output is
effectively zero. Thus, if m(t) is the message (sine) and c(t) is a 10 kHz square-wave carrier (0/1 levels), the
switch produces:

vswitch (t) = m(t) x(t),

where x(t) is a rectangular waveform that is 1 during the carrier’s high interval and 0 during its low
interval. This means the output alternates between the message waveform and zero—it “gates” the message.
In the time domain, the output voltage follows the shape of the message during ON periods and is zero
during OFF periods. This non-linear switching thus effectively multiplies the message by the square carrier.
As a result, the output contains frequency components at the carrier frequency and its harmonics, modulated
by the message spectrum.

4.2 Mathematics (Fourier Analysis)

The 10 kHz square carrier (50% duty, toggling between 0 and 1) can be represented as a Fourier series. For
a square wave x(t) of fundamental frequency fc :
1 2 2 2
x(t) = + cos(2πfc t) − cos(6πfc t) + cos(10πfc t) − · · ·
2 π 3π 5π
Multiplying the message m(t) by x(t) yields:
1 2 2
vswitch (t) = m(t)x(t) = m(t) + m(t) cos(2πfc t) − m(t) cos(6πfc t) + · · ·
2 π 3π
In the frequency domain, this corresponds to the baseband message spectrum around 0 Hz (from the 21
term), and copies of the message spectrum centered at ±fc , ±3fc , ±5fc , etc. (from the cosine terms).
To extract a clean AM signal, we use a band-pass filter centered at the carrier frequency. An ideal band-
pass filter of appropriate bandwidth will pass only the components around fc and reject DC and higher
harmonics. In the idealized case (assuming the first term at DC and higher harmonics are removed), the
output of the filter is:
2
s(t) =m(t) cos(2πfc t),
π
which is a conventional amplitude-modulated signal. In practice, the amplitude is scaled by 2/π (≈0.64)
due to the Fourier coefficient. The band-pass filter isolates this ±fc component, yielding the AM wave
∝ m(t) cos(2πfc t) with the message as its envelope.

4.3 Band-Pass Filter

The multiple-feedback band-pass filter (MFB BPF) is used to select the carrier frequency component
and shape the frequency response. Its purpose is to pass frequencies near fc (10 kHz) and reject both the
baseband (DC) and higher-order terms from the switching process. In this design, we set F0 = 10 kHz
(center frequency) and quality factor Q = 5. The general transfer function of an MFB band-pass filter (with
capacitors C3 , C4 and resistors R1 , R2 , R5 ) is:

Vo (s) s
H(s) = = 2 C3 +C4

.
+ RR5 C1 C3 C4 4 1 1


Vi (s) s +s C3 C4 R5 R1 + R2

By choosing C3 = C4 = 1.0 nF and using standard design relations, we derive the component values
for the desired F0 , Q, and gain. (See the next section for detailed calculations.) The filter’s bandwidth

2
is B = F0 /Q = 2000 Hz, so it passes a 2 kHz band around 10 kHz. Its peak gain H = 1 is set to unity
(no amplification) for simplicity. The filter suppresses the unwanted frequency components from the raw
switching output, so that primarily the cos(2πfc t) term remains.

5 Circuit Design and Calculations

(Insert circuit diagram here)

Figure 1: Circuit diagram of Switching Modulation Circuit

(Insert circuit diagram here)

Figure 2: Circuit diagram of Band Pass Filter

5.1 Filter Design

We use the multiple-feedback band-pass design procedure. Let F0 = 10 kHz, Q = 5, C3 = C4 = 1.0 nF, and
assume unity midband gain H = 1. We compute:

• k = 2πF0 C3 = 2π(10 000 Hz)(1.0 × 10−9 F) = 6.283 × 10−5 s−1 .

• R1 = 1
Hk = 1
1×6.283×10−5 ≈ 1.59 × 104 Ω ≈ 16 kΩ.

• R2 = 1
(2Q−H) k = 1
(2×5−1)(6.283×10−5 ) ≈ 1.77 × 103 Ω ≈ 1.8 kΩ.

• R5 = 2Q
k = 10
6.283×10−5 ≈ 1.59 × 105 Ω ≈ 160 kΩ.

These values are rounded to practical resistors (e.g., R1 = 16 kΩ, R2 = 1.8 kΩ, R5 = 160 kΩ). Using these,
the filter’s center frequency is F0 = 10 kHz (by design), its Q = 5, and bandwidth B = F0 /Q = 2.0 kHz. The
expected midband gain is 1.0 (0 dB).

3
5.2 Complete Circuit
The full modulator circuit consists of the following stages:
• Message input: A 1 kHz sine wave (4 Vpp) from Generator 1 is applied to the transistor input
(collector) via a coupling resistor.

• Carrier drive: A 10 kHz square wave (50% duty, 4 Vpp) from Generator 2 is applied to the transistor
base (through a base resistor) to switch it ON/OFF.
• Transistor switch: The NPN transistor alternately connects/disconnects the message to the output
node. When the base is high, the transistor saturates and the message appears at the collector output;
when the base is low, the transistor cuts off and the output is near 0 V.
• Buffer/Filter: The pulsed output is fed into the LM741 op-amp configured as the MFB band-pass
filter. Capacitors C3 and C4 (1 nF each) and resistors R1 , R2 , R5 implement the 10 kHz band-pass
response.
• Output: The op-amp filter output is the final AM signal. It has a 10 kHz carrier whose amplitude is
modulated by the 1 kHz message. This output is observed on the oscilloscope.

6 Results and Discussion

(Insert oscilloscope output at buffer here)

Figure 3: Output waveform observed at buffer stage

4
 (Insert FFT of buffer output here)

Figure 4: FFT analysis of buffer output

(Insert modulated output signal here)

Figure 5: Final modulated output waveform

5
 (Insert FFT of modulated signal here)

Figure 6: FFT analysis of modulated output

6.1 Observations
• The oscilloscope clearly shows a 10kHz carrier wave successfully modulated by the 1kHz input signal,
with the envelope perfectly following the message waveform.
• FFT analysis reveals the expected spectral components at the carrier frequency (10kHz) and its side-
bands (9kHz and 11kHz), confirming proper amplitude modulation.
• Visible harmonic distortion at 30kHz (third harmonic) is observed, which is characteristic of square-
wave switching modulation.

• The time-domain waveform shows stable periodicity with minimal distortion, indicating proper circuit
operation and clean switching action.

7 Discussion
The experiment showed how we can create AM signals using a simple JFET switching circuit and a second
order band-pass filter. We used a 1kHz sound wave to change the strength of a 10kHz carrier wave. The
buffer before the filter helped in impedence matching to decrease loading effects. We saw clear AM signals
on the oscilloscope - the 10kHz wave’s height changed exactly with our 1kHz sound. The frequency analysis
showed the main signal at 10kHz with side signals at 9kHz and 11kHz, plus some extra unwanted frequencies
at 30kHz that always appear in this type of circuit. The filter did its job by removing most of these unwanted
frequencies while keeping our AM signal clean. This proves switching modulators work well for AM, but we
need good buffers and filters to get clean signals for real radio systems.