How does a quadrature amplitude demodulator work?
2 Answers
A **quadrature amplitude demodulator** (QAM demodulator) is a device used to decode a signal modulated using **Quadrature Amplitude Modulation (QAM)**. QAM combines both **amplitude modulation (AM)** and **phase modulation** to encode data in both the amplitude and phase of the carrier signal. Here's a step-by-step breakdown of how a QAM demodulator works:
### 1. **Input Signal:**
- The received signal is a QAM-modulated signal that contains information encoded in both its **amplitude** and **phase**. This signal can be expressed as:
\[
s(t) = A \cos(2\pi f_c t + \theta)
\]
where:
- \( A \) is the amplitude (which carries part of the information),
- \( \theta \) is the phase shift (which carries additional information),
- \( f_c \) is the carrier frequency.
### 2. **Local Oscillator (LO):**
The demodulator generates two reference signals using a local oscillator at the carrier frequency \( f_c \):
- A **cosine wave**: \( \cos(2\pi f_c t) \),
- A **sine wave**: \( \sin(2\pi f_c t) \).
### 3. **Mixing with Carrier Signals (Product Demodulation):**
The received QAM signal is multiplied (mixed) with both the in-phase and quadrature signals from the local oscillator:
- **In-phase signal**: The received signal is mixed with the cosine wave:
\[
I(t) = s(t) \cdot \cos(2\pi f_c t)
\]
This results in the **in-phase component** \( I(t) \), which corresponds to the amplitude-modulated information aligned with the carrier wave.
- **Quadrature signal**: The received signal is mixed with the sine wave:
\[
Q(t) = s(t) \cdot \sin(2\pi f_c t)
\]
This gives the **quadrature component** \( Q(t) \), which represents the information encoded in the phase shift of the signal.
### 4. **Low-pass Filtering:**
After mixing, the signal contains a high-frequency component (at twice the carrier frequency, \( 2f_c \)) and a low-frequency component. A low-pass filter is applied to remove the high-frequency components, leaving only the baseband in-phase (I) and quadrature (Q) signals.
### 5. **Extraction of Information:**
- The in-phase \( I(t) \) and quadrature \( Q(t) \) components represent the information encoded in the amplitude and phase of the original QAM signal.
- Together, \( I(t) \) and \( Q(t) \) can be used to reconstruct the data by determining both the amplitude and phase of the signal at any given time.
### 6. **Mapping to Symbol Constellation:**
- The \( I \) and \( Q \) components are used to map the signal onto a **constellation diagram**, where each point represents a unique combination of amplitude and phase, corresponding to a symbol (group of bits).
- The demodulator then converts these symbols back into the corresponding bitstream.
### Summary:
- The quadrature amplitude demodulator splits the incoming QAM signal into its in-phase and quadrature components using mixing and low-pass filtering.
- These components represent the encoded data, which is decoded by mapping them back to their original symbol form using the QAM constellation.
This method allows QAM to transmit more data efficiently by encoding information in both amplitude and phase.
### 1. **Input Signal:**
- The received signal is a QAM-modulated signal that contains information encoded in both its **amplitude** and **phase**. This signal can be expressed as:
\[
s(t) = A \cos(2\pi f_c t + \theta)
\]
where:
- \( A \) is the amplitude (which carries part of the information),
- \( \theta \) is the phase shift (which carries additional information),
- \( f_c \) is the carrier frequency.
### 2. **Local Oscillator (LO):**
The demodulator generates two reference signals using a local oscillator at the carrier frequency \( f_c \):
- A **cosine wave**: \( \cos(2\pi f_c t) \),
- A **sine wave**: \( \sin(2\pi f_c t) \).
### 3. **Mixing with Carrier Signals (Product Demodulation):**
The received QAM signal is multiplied (mixed) with both the in-phase and quadrature signals from the local oscillator:
- **In-phase signal**: The received signal is mixed with the cosine wave:
\[
I(t) = s(t) \cdot \cos(2\pi f_c t)
\]
This results in the **in-phase component** \( I(t) \), which corresponds to the amplitude-modulated information aligned with the carrier wave.
- **Quadrature signal**: The received signal is mixed with the sine wave:
\[
Q(t) = s(t) \cdot \sin(2\pi f_c t)
\]
This gives the **quadrature component** \( Q(t) \), which represents the information encoded in the phase shift of the signal.
### 4. **Low-pass Filtering:**
After mixing, the signal contains a high-frequency component (at twice the carrier frequency, \( 2f_c \)) and a low-frequency component. A low-pass filter is applied to remove the high-frequency components, leaving only the baseband in-phase (I) and quadrature (Q) signals.
### 5. **Extraction of Information:**
- The in-phase \( I(t) \) and quadrature \( Q(t) \) components represent the information encoded in the amplitude and phase of the original QAM signal.
- Together, \( I(t) \) and \( Q(t) \) can be used to reconstruct the data by determining both the amplitude and phase of the signal at any given time.
### 6. **Mapping to Symbol Constellation:**
- The \( I \) and \( Q \) components are used to map the signal onto a **constellation diagram**, where each point represents a unique combination of amplitude and phase, corresponding to a symbol (group of bits).
- The demodulator then converts these symbols back into the corresponding bitstream.
### Summary:
- The quadrature amplitude demodulator splits the incoming QAM signal into its in-phase and quadrature components using mixing and low-pass filtering.
- These components represent the encoded data, which is decoded by mapping them back to their original symbol form using the QAM constellation.
This method allows QAM to transmit more data efficiently by encoding information in both amplitude and phase.