Intermediate Frequency (IF) Sampling Receiver Concepts

Intermediate Frequency (IF) Sampling Receiver Concepts
Mark Rives, Principal Applications Engineer

This article will discuss Intermediate Frequency (IF) sampling concepts of sub-sampling (or under sampling), noise processing gain, and the effects of interfering signals. Examples will be based on the GSM/EDGE communications standard where the channel bandwidth is 200 kHz and the sample rate is typically a multiple of 13 MHz.

Sub-Sampling

Nyquist's sampling theorem states that if a signal is sampled at least twice as fast as the highest sampled frequency component, no information will be lost when the signal is reconstructed. The sample rate divided by two (Fs/2) is known as the Nyquist frequency and the frequency range from DC (or 0 Hz) to Fs/2 is called the first Nyquist zone.

Figure 1. Nyquist Sampling Example

We’ll use National's high-speed ADC12DL080 as an example. Clocking the ADC12DL080 at 6 * 13 MHz or 78 Mega-Samples Per Second (MSPS) places the Nyquist frequency at 39 MHz. All the signal information that falls in the first Nyquist zone is over sampled and can be recovered. If the sampled signal moves into the second Nyquist zone from 39 MHz to 78 MHz, it can still be recovered but the absolute frequency information is lost. When the input signal moves above Fs/2, it has been sub-sampled and ‘reflects’ or ‘folds’ at Fs/2 and moves back toward 0 Hz at the ADC output. If Fs/2 = 39 MSPS, an input signal at 40 MHz will fold back to 38 MHz. Folding will occur in each Nyquist zone. For example, a 244 MHz IF at 78 MSPS will result in a 10 MHz signal at the ADC output. The folded (or aliased) frequency is calculated by finding the closest multiple of Fs to the desired input frequency (FIN, 244 MHz), then subtracting the two frequencies:

F_IN = (n * Fs) or 244 MHz – (3 * 78 MHz)
= 244 MHz – 234 MHz = 10 MHz

Signals at 10 MHz, 68 MHz, 88 MHz, 146 MHz, and beyond will all appear at 10 MHz. There is no way to determine the original IF since the Nyquist criteria has been violated.

Sub-sampling systems take advantage of this folding or mixing function to reduce the IF frequency prior to a final digital tuner like National's CLC5903. If the desired signal Bandwidth (BW) is less than Fs/2, all of the signal information can still be recovered. A channel filter should be placed in front of the ADC to remove any undesired signals from other Nyquist zones. This filter will also limit the amount of noise at the ADC input to only one Nyquist zone.

Noise Processing Gain

Figure 2. Noise Processing Gain

As the ADC input frequency increases, the Signal-to-Noise Ratio (SNR) for large signals will decrease due to clock jitter. Small signal SNR is not affected. For the ADC12DL080, the large signal SNR will be 65 dBFS (dB relative to Full Scale) at a 244 MHz IF. When the IF Sampling Receiver Concepts input is reduced to -10 dBFS or less, the SNR will increase to 70 dBFS. If the desired channel bandwidth is over sampled, a digital channel filter can further improve the SNR. When an ADC's SNR is measured, it is normally specified as the SNR in the first Nyquist zone. In other words, all the noise from DC to Fs/2 is summed to get the SNR relative to the ADC’s full-scale input. A digital channel filter can remove the ADC output noise except in the channel bandwidth. The output noise is integrated over a smaller frequency range. This improvement is called noise processing gain and can be calculated with the following equation:

Processing Gain = -10 * LOG (Channel BW/Nyquist BW)

For a 200 kHz narrow-band system:

Processing Gain = -10 * LOG (200 kHz/39 MHz) = 22.9 dB

Processing gain can also be calculated by finding the noise floor of the ADC in dBm/Hz. With an IF of 244 MHz at -1 dBFS, the SNR of the ADC12DL080 is 65 dBFS or -55 dBm since full scale is +10 dBm into 50W. To translate into dBm/Hz, take 10 * LOG (Fs/2) and subtract it from -55 dBm. 10 * LOG (39 MHz) = 75.9 dB, therefore the ADC12DL080 noise floor in this example is -130.9 dBm/Hz. Now if the channel bandwidth is 200 kHz, add back 10 * LOG (200 kHz) or 53 dB to get a noise floor of -77.9 dBm in 200 kHz, which is 22.9 dB better than the ADC by itself. Translating back to dBFS, the total SNR is 87.9 dB in a 200 kHz channel. This is similar to decreasing the resolution bandwidth on a spectrum analyzer; the noise floor has been lowered, but the ADC’s resolution has not been increased.

Interfering Signals

GSM systems require the receiver to operate with signals from -13 dBm to -104 dBm when there are no interfering signals. Typical receivers need some extra margin to demodulate the received signal. This is called the Carrier-to-Interferer (C/I) ratio and is 9 dB for GSM. This means that the noise floor must be below -113 dBm, resulting in a dynamic range of greater than 100 dB, which is more than our ADC can provide. Normally a Variable Gain Amplifier (VGA) is added to the system to scale the input signal to the ADC.

Figure 3. Channel Filter

Adding a VGA works well until a large interfering signal is present. In GSM systems, this condition can occur when one subscriber is close to the basestation and one is far away. The close subscriber may actually be talking to a more distant basestation on an adjacent channel, which can block the reception of the weak signal. Hence, the large signal is known as a blocker. The blocker can be up to -13 dBm while the weak signal can be as low as -101 dBm. Considering the 9 dB C/I ratio, the overall dynamic range requirement is now -13 dBm – ( -110 dBm) or 97 dB with a blocking signal. If the blocker causes the VGA gain to decrease to prevent clipping the ADC input, the weak signal can be lost in the noise.

The channel filter in front of the ADC will reduce the level of the blocking signal, but the ADC will still operate near full scale. Clock jitter and the large signal will degrade the SNR causing a loss of sensitivity if the filter rejection of the blocker is not sufficient.

Summary

High-speed ADCs such as the ADC12DL080 combined with a digital tuner such as the CLC5903 can simplify receiver design and provide excellent performance for high dynamic range signals. More information on this topic is available in the LDRCS user's guide.