1. Chapter4 Bandpass Signalling Bandpass Filtering and Linear Distortion
Amplifiers and Nonlinear Distortion
Total Harmonic Distortion (THD)
Intermodulation Distortion (IMD)
Huseyin Bilgekul
Eeng360 Communication Systems I
Department of Electrical and Electronic Engineering
Eastern Mediterranean University

2. Bandpass Filtering and Linear Distortion
Equivalent Low-pass filter: Modeling a bandpass filter by using an equivalent low pass filter (complex impulse response)
Bandpass filter
H(f) = Y(f)/X(f)
Input bandpass waveform
Output bandpass waveform
Impulse response of the bandpass filter
Frequency response of the bandpass filter

3. Bandpass Filtering

4. Bandpass Filtering Theorem:
The complex envelopes for the input, output, and impulse response of a bandpass filter are related by
g1(t) – complex envelope of input
k(t) – complex envelope of impulse response
Also,
Proof:
Spectrum of the output is
Spectra of bandpass waveforms are related to that of their complex enveloped
But

5. Bandpass Filtering Thus, we see that
Taking inverse fourier transform on both sides
Any bandpass filter may be described and analyzed by using an equivalent low-pass filter.
Equations for equivalent LPF are usually much less complicated than those for bandpass filters & so the equivalent LPF system model is very useful.

6. Linear Distortion
For distortionless transmission of bandpass signals, the channel transfer function H(f) should satisfy the following requirements:
The amplitude response is constant
A- positive constant
The derivative of the phase response is constant
Tg – complex envelope delay
Integrating the above equation, we get

7. Linear Distortion

8. Bandpass filter delays input info by Tg , whereas the carrier by Td
Linear Distortion
The channel transfer function is
If the input to the bandpass channel is
Then the output to the channel (considering the delay Tg due to ) is
Using
Phase response of a
linear function
of frequency
Bandpass filter delays input info by Tg , whereas the carrier by Td
Modulation on the carrier is delayed by Tg & carrier by Td

9. Received Signal Pulse The signal out of the transmitter
Transmission
medium
(Channel)
Carrier
circuits
Signal
processing
Information m
input
The signal out of the transmitter
g(t) – Complex envelope of v(t)
If the channel is LTI , then received signal + noise
n(t) – Noise at the receiver input
Signal + noise at the receiver input
A – gain of the channel
- carrier phase shift caused by the channel, Tg – channel group delay.
Signal + noise at the receiver input

10. Nonlinear Distortion Amplifiers Non-linear Linear
Circuits with memory and circuits with no memory
Memory - Present output value ~ function of present input + previous input values
- contain L & C
No memory - Present output values ~ function only of its present input values.
Circuits : linear + no memory – resistive ciruits
linear + memory – RLC ciruits (Transfer function)

11. Nonlinear Distortion
Assume no memory  Present output as a function of present input in ‘t’ domain
If the amplifier is linear
K- voltage gain of the amplifier
In practice, amplifier output becomes saturated as the amplitude of the input signal is increased.
output-to-input characteristic can be modelled as a Taylor’s expansion about vi =0
Where
- output dc offset level
- 1st order (linear) term
- 2nd order (square law) term
There will be nonlinear distortion on the output if K2,K3,… are non-zero.

12. 2nd Harmonic Distortion with
Nonlinear Distortion
Harmonic Distortion associated with the amplifier output is determined by
Applying a single sinusoidal test tone to the amplifier input
Let the input test tone be represented by
To the amplifier input
Then the second-order output term is
2nd Harmonic Distortion with =
In general, for a single-tone input, the output will be
Vn – peak value of the output at the frequency nf0
The Percentage Total Harmonic Distortion (THD) of an amplifier is defined by

13. Nonlinear Distortion
Intermodulation distortion (IMD) of the amplifier is obtained by using a two-tone test signal :
If the input (tone) signals are
Then the second-order output term is
IMD
Harmonic distortion at 2f1 & 2f2
Second-order IMD is: