# Communication Systems/AM Receivers

## AM Receivers

The most common receivers in use today are the super heterodyne type.
They consist of:

::\*Antenna

::\*RF amplifier

::\*Local Oscillator and Mixer

::\*IF Section

::\*Detector and Amplifier

The need for these subsystems can be seen when one considers the much
simpler and inadequate TRF or tuned radio frequency amplifier.

### TRF Amplifier

It is possible to design an RF amplifier to accept only a narrow range
of frequencies, such as one radio station on the AM band.

:   

    :   ![](TRF_amplifier.gif "fig:TRF_amplifier.gif")

By adjusting the center frequency of the tuned circuit, all other input
signals can be excluded.

:   

    :   ![](Channel_selection.gif "fig:Channel_selection.gif")

The AM band ranges from about 500 kHz to 1600 kHz. Each station requires
10 kHz of this spectrum, although the baseband signal is only 5 kHz.

Recall that for a tuned circuit: $Q = \frac{{f_c }}{B}$. The center or
resonant frequency in an RLC network is most often adjusted by varying
the capacitor value. However, the Q remains approximately constant as
the center frequency is adjusted. This suggests that as the bandwidth
varies as the circuit is tuned.

:   

    :   For example, the Q required at the lower end of the AM band to
        select only one radio station would be approximately:

$$Q = \frac{{f_c }}{B} = \frac{{500\;kHz}}{{10\;kHz}} = 50$$

:   

    :   As the tuned circuit is adjusted to the higher end of the AM
        band, the resulting bandwidth is:

$$B = \frac{{f_c }}{Q} = \frac{{1600\;kHz}}{{50}} = 30\;kHz$$

A bandwidth this high could conceivably pass three adjacent stations,
thus making meaningful reception impossible.

To prevent this, the incoming RF signal is heterodyned to a fixed IF or
intermediate frequency and passed through a constant bandwidth circuit.

### Superheterodyne Receiver

:   

    :   ![](Heterodyne.gif "fig:Heterodyne.gif")

The RF amplifier boosts the RF signal into the mixer. It has broad
tuning and amplifies not just one RF station, but many of them
simultaneously. It also amplifies any input noise and even contributes
some of its own.

The other mixer input is a high frequency sine wave created by a local
oscillator. In AM receivers, it is always 455 kHz above the desired
station carrier frequency. An ideal mixer will combine the incoming
carrier with the local oscillator to create sum and difference
frequencies. .

A real mixer combines two signals and creates a host of new frequencies:

:   

    :   • A dc level
    :   • The original two frequencies
    :   • The sum and difference of the two input frequencies
    :   • Harmonics of the two input frequencies
    :   • Sums and differences of all of the harmonics

Since the RF amplifier passes several radio stations at once, the mixer
output can be very complex. However, the only signal of real interest is
the difference between the desired station carrier frequency and the
local oscillator frequency. This difference frequency, also called the
IF (intermediate frequency) will alway be 455 kHz. By passing this
through a 10 kHz BPF (band pass filter) centered at 455 kHz, the bulk of
the unwanted signals can be eliminated.

#### Local Oscillator Frequency

Since the mixer generates sum and difference frequencies, it is possible
to generate the 455 kHz IF signal if the local oscillator is either
above or below the IF. The inevitable question is which is preferable.

:   

    :   **Case I The local Oscillator is above the IF.** This would
        require that the oscillator tune from (500 + 455) kHz to
        (1600 + 455) kHz or approximately 1 to 2 MHz. It is normally the
        capacitor in a tuned RLC circuit, which is varied to adjust the
        center frequency while the inductor is left fixed.

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:   

    :   Since $f_c  = \frac{1}{{2\pi \sqrt {LC} }}$

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:   

    :   solving for *C* we obtain
        $C = \frac{1}{{L\left( {2\pi f_c } \right)^2 }}$

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:   

    :   When the tuning frequency is a maximum, the tuning capacitor is
        a minimum and vice versa. Since we know the range of frequencies
        to be created, we can deduce the range of capacitance required.

$$\frac{{C_{\max } }}{{C_{\min } }} = \frac{{L\left( {2\pi f_{\max } } \right)^2 }}{{L\left( {2\pi f_{\min } } \right)^2 }} = \left( {\frac{{2\;MHz}}{{1\;MHz}}} \right)^2  = 4$$

Making a capacitor with a 4:1 value change is well within the realm of
possibility.

:   

    :   **Case II The local Oscillator is below the IF**. This would
        require that the oscillator tune from (500 - 455) kHz to
        (1600 - 455) kHz or approximately 45 kHz to 1145 kHz, in which
        case:

$$\frac{{C_{\max } }}{{C_{\min } }} = \left( {\frac{{1145\;kHz}}{{45\;kHz}}} \right)^2  \approx 648$$

It is not practical to make a tunable capacitor with this type of range.
Therefore the local oscillator in a standard AM receiver is above the
radio band.

#### Image Frequency

Just as there are two oscillator frequencies, which can create the same
IF, two different station frequencies can create the IF. The undesired
station frequency is known as the image frequency.

;;;![](Image_frequency.gif "Image_frequency.gif")

If any circuit in the radio front end exhibits non-linearities, there is
a possibility that other combinations may create the intermediate
frequency. Once the image frequency is in the mixer, there is no way to
remove it since it is now heterodyned into the same IF band as the
desired station.

### AM Detection

There are two basic types of AM detection, coherent and non-coherent. Of
these two, the non-coherent is the simpler method.

::\*Non-coherent detection does not rely on regenerating the carrier
signal. The information or modulation envelope can be removed or
detected by a diode followed by an audio filter.

::\*Coherent detection relies on regenerating the carrier and mixing it
with the AM signal. This creates sum and difference frequencies. The
difference frequency corresponds to the original modulation signal.

Both of these detection techniques have certain drawbacks. Consequently,
most radio receivers use a combination of both.

#### Envelope Detector

:   

    :   ![](Envelope_detector.gif "fig:Envelope_detector.gif")

An envelope detector is simply a half wave rectifier followed by a low
pass filter. In the case of commercial AM radio receivers, the detector
is placed after the IF section. The carrier at this point is 455 kHz
while the maximum envelope frequency is only 5 kHz. Since the ripple
component is nearly 100 times the frequency of the highest baseband
signal and does not pass through any subsequent audio amplifiers.

:   

    :   An AM signal where the carrier frequency is only 10 times the
        envelope frequency would have considerable ripple:

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:   

    :   ![](Exagerated_am_ripple.gif "fig:Exagerated_am_ripple.gif"){width="300"}

#### Synchronous Detector

In a synchronous or coherent detector, the incoming AM signal is mixed
with the original carrier frequency.

:   

    :   ![](Synchronous_detector.gif "fig:Synchronous_detector.gif")

If you think this looks suspiciously like a mixer, you are absolutely
right! A synchronous detector is one where the difference frequency
between the two inputs is zero Hz. Of in other words, the two input
frequencies are the same. Let\'s check the math.

Recall that the AM input is mathematically defined by:

$$e_{am}  = \underbrace {\sin \omega _c t}_{{\rm{Carrier}}} + \underbrace {\frac{m}{2}\sin \left( {\omega _c  - \omega _m } \right)t}_{{\rm{Lower}}\;{\rm{Sideband}}} - \underbrace {\frac{m}{2}\sin \left( {\omega _c  + \omega _m } \right)t}_{{\rm{Upper}}\;{\rm{Sideband}}}$$

:   

    :   At the multiplier output, we obtain:

$${\rm{mixer}}\;{\rm{out  =  }}e_{am}  \times \sin \omega _c t = \underbrace { - \frac{m}{2}\sin \omega _m t}_{{\rm{Original}}\;{\rm{Modulation}}\;{\rm{Signal}}}\underbrace { - \frac{1}{2}\sin 2\omega _c t - \frac{m}{4}\sin \left( {2\omega _c  - \omega _m } \right)t + \frac{m}{4}\sin \left( {2\omega _c  + \omega _m } \right)t}_{{\rm{AM}}\;{\rm{signal}}\;{\rm{centered}}\;{\rm{at}}\;{\rm{2}}\;{\rm{times}}\;{\rm{the}}\;{\rm{carrier}}\;{\rm{frequency}}}$$

:   

    :   The high frequency component can be filtered off leaving only
        the original modulation signal.

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:   

    :   This technique has one serious drawback. The problem is how to
        create the exact carrier frequency. If the frequency is not
        exact, the entire baseband signal will be shifted by the
        difference. A shift of only 50 Hz will make the human voice
        unrecognizable. It is possible to use a PLL (phase locked loop),
        but making one tunable for the entire AM band is not trivial.

As a result, most radio receivers use an oscillator to create a fixed
intermediate frequency. This is then followed by an envelope detector or
a fixed frequency PLL.

#### Squaring Detector

The squaring detector is also a synchronous or coherent detector. It
avoids the problem of having to recreate the carrier by simply squaring
the input signal. It essentially uses the AM signal itself as a sort of
wideband carrier.

:   

    :   ![](Squaring_detector.gif "fig:Squaring_detector.gif")

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:   

    :   The output of the multiplier is the square of the input AM
        signal:

$$\left( {e_{am} } \right)^2  = \left( {\sin \omega _c t + \frac{m}{2}\sin \left( {\omega _c  - \omega _m } \right)t - \frac{m}{2}\sin \left( {\omega _c  + \omega _m } \right)t} \right)^2$$

Since the input is being multiplied by the ${\sin \omega _c t}$
component, one of the resulting difference terms is the original
modulation signal. The principle difficulty with this approach is trying
to create a linear, high frequency multiplier.

