5.1.1.3 Estimation of Maximum Frequency Offset Between Receiver and Transmitter

The required channel filter bandwidth depends on the frequency error between the receiver and transmitter and the occupied bandwidth of the modulation signal used. For ASK systems, a frequency transition during the power amplifier switching has to be additionally taken into account if the ATA8710 is used as the ASK transmitter. For more details, see the ASK considerations in the second part of this section.

For more details regarding the main impact of the XTO on the worst case frequency error between the receiver and transmitter, see System Design with Compensation of Initial XTAL and XTO Tolerances from Related Links. The maximum frequency error between the receiver and transmitter has to be determined for the individual application, and the channel filter bandwidth has to be chosen with enough width to prevent the unintentional loss of sensitivity, in the case of worst case frequency errors. The channel bandwidths of the ATA8210/15 can be configured between 25 kHz and 360 kHz. See Channel Filter Bandwidths in the Channel Filter from Related Links.

The following table shows the measured frequency offset values with 1.5 dB sensitivity loss for FSK systems compared with values calculated using equation (51). If using NRZ encoding instead of Manchester encoding, equation (51) can be used, replacing data rate (DR) by symbol rate (SR). The calculated maximum frequency offset differs from measurement in cases of high occupied bandwidth compared to the channel filter bandwidth and in cases of high modulation indices. This behavior is a property of the RxDSP; therefore, it is highly reproducible and a measurement result can be used for system design without the need to consider part-to-part variations.

{Δ f}_{S 1.5 d B F S K} = \frac{{B W}_{I F}}{2} - \sqrt{{D R}_{F S K}^{2} + {f_{D E V}}^{2}} (51)

D R = \frac{S R}{2} (52)

Table 5-1. Filter Settings for Each Supported IF Bandwidth
Channel Filter Bandwidth	Manchester-Coded FSK Data Rate and Frequency Deviation	Measured Frequency Offset Δf_{S1.5dBFSK_measured}	Calculated Frequency Offset with Equation
25 kHz	0.75 kBit ±0.75 kHz	±10.7 kHz	±11.44 kHz
	2.4 kBit ±2.4 kHz	±9.4 kHz	±9.10 kHz
	5 kBit ±2.4 kHz	±6.8 kHz	±6.95 kHz
80 kHz	2.4 kBit ±2.4 kHz	±35 kHz	±36.6 kHz
	10 kBit ±10 kHz	±27.5 kHz	±25.8 kHz
	20 kBit ±20 kHz	±17.5 kHz	±11.7 kHz
165 kHz	5 kBit ±5 kHz	±72.5 kHz	±75.4 kHz
	10 kBit ±10 kHz	±70 kHz	±68.3 kHz
	20 kBit ±20 kHz	±57.5 kHz	±54.2 kHz
	1 kBit ±16 kHz	±60 kHz	±66.5 kHz
	10 kBit ±16 kHz	±70 kHz	±63.6 kHz
366 kHz	10 kBit ±10 kHz	±170 kHz	±168.8 kHz
	20 kBit ±20 kHz	±155 kHz	±154.7 kHz
	10 kBit ±38 kHz	±135 kHz	±143.7 kHz

The following figure shows the sensitivity loss versus frequency offset for FSK with DR = 2.4 kBit/s and f_DEV = ±2.4 kHz using a 80 kHz channel filter bandwidth. The 1.5 dB additional loss in the link budget can be avoided using a slightly higher bandwidth. For more details, see System Design with Compensation of Initial XTAL and XTO Tolerances from Related Links. In the 80 kHz bandwidth, FSK DR = 2.4 kBit/s and f_DEV = ±2.4 kHz case using only ±30 kHz maximum frequency offset instead of ±35 kHz avoids the additional 1.5 dB sensitivity loss in the link budget. For the other channel filter bandwidth and data rate examples, the behavior is equivalent. This can be taken into account by lowering the maximum frequency offset by BW_IF/16. Equation (53) must be used to incorporate this into the system design. The ripple in the sensitivity in the following figure is caused by ±0.5 dB measurement uncertainty and is not a property of the ATA8210/15.

Figure 5-1. Measured Sensitivity Loss Versus Frequency Offset (BW = 80 kHz, FSK, DR = 2.4 kBit/s, f_DEV = ±2.4 kHz)

The following figure shows the sensitivity loss versus frequency offset for DR = 10 kBit/s and f_DEV = ±10 kHz using a 165 kHz channel filter bandwidth. The ripple in the sensitivity in the following figure is caused by ±0.5 dB measurement uncertainty and is not a property of the ATA8210/15.

Figure 5-2. Measured Sensitivity Loss Versus Frequency Offset (BW = 165 kHz, FSK, DR = 10 kBit/s, f_DEV = ±10 kHz)

{Δ f}_{\max F S K} = \frac{{B W}_{I F}}{2} - \sqrt{{D R}_{F S K}^{2} + {f_{D E V}}^{2}} - \frac{{B W}_{I F}}{16} (53)

The following table shows the measured and calculated maximum frequency offsets derived from equation (52) for low loss in sensitivity. Microchip recommends using these numbers for system design.

Table 5-2. Measured Frequency Offset for Low Sensitivity Loss Using an FSK System
Channel Filter Bandwidth	Manchester Coded FSK Data Rate and Frequency Deviation	Recommended maximum Frequency Offset for Low Loss Based on Measurement	Calculated Frequency Offset with Equation
25 kHz	0.75 kBit ±0.75 kHz	±9.1 kHz	±9.9 kHz
	2.4 kBit ±2.4 kHz	±7.8 kHz	±7.5 kHz
	5 kBit ±2.4 kHz	±5.2 kHz	±5.4 kHz
80 kHz	2.4 kBit ±2.4 kHz	±30 kHz	±31.6 kHz
	10 kBit ±10 kHz	±22.5 kHz	±20.8 kHz
	20 kBit ±20 kHz	±12.5 kHz	±6.7 kHz
165 kHz	5 kBit ±5 kHz	±62.2 kHz	±65.1 kHz
	10 kBit ±10 kHz	±59.7 kHz	±58 kHz
	20 kBit 20 kHz	±47.2 kHz	±43.9 kHz
	1 kBit 16 kHz	±49.7 kHz	±56.2 kHz
	10 kBit ±16 kHz	±59.7 kHz	±53.3 kHz
366 kHz	10 kBit ±10 kHz	±147 kHz	±145.9 kHz
	20 kBit ±20 kHz	±132 kHz	±131.8 kHz
	10 kBit ±38 kHz	±112 kHz	±120.8 kHz

The following table shows the measured frequency offset values for 1.5 dB sensitivity loss compared with values calculated with equation (57). The calculated maximum frequency offsets are, in most cases, lower than the measured ones. Therefore, the calculated maximum frequency offsets can be used for system design using ASK.

{Δ f}_{S 1.5 d B A S K} = \frac{{B W}_{I F}}{2} - {D R}_{A S K} (57)

Table 5-3. Frequency Offset for 1.5 dB Sensitivity Loss Using an ASK System
Channel Filter Bandwidth	Manchester Coded ASK Data Rate	Measured Frequency Offset Δf_{S1.5dBASK_measured}	Calculated Frequency Offset with Equation (56)
25 kHz	2.4 kBit/s	±11.2 kHz	±10.1 kHz
25 kHz	5 kBit/s⁽¹⁾	±11.2 kHz⁽¹⁾	±7.5 kHz
80 kHz	2.4 kBit/s	±37.5 kHz	±37.6 kHz
	10 kBit/s	±36 kHz	±30 kHz
	20 kBit/s⁽¹⁾	±36 kHz⁽¹⁾	±20 kHz
165 kHz	2.4 kBit/s	±77.5 kHz	±80 kHz
165 kHz	20 kBit/s	±66 kHz	±62.5 kHz
366 kHz	2.4 kBit/s	±180 kHz	±180.6 kHz
366 kHz	20 kBit/s	±170 kHz	±163 kHz
Note: In the case of high ASK data rates compared with the bandwidth, the sensitivity versus frequency offset curve is not as flat as in other cases. For these data rates, the frequency offset for 3 dB loss of sensitivity is given in this table and the following table.

The following figure shows the sensitivity versus frequency offset for ASK with DR = 2.4 kBit/s using 165 kHz channel filter bandwidth. The 1.5 dB additional loss in the link budget can also be avoided using the BW_IF/16 lower frequency offset, as in the FSK case; therefore, equation (58) must be used for system design.

Figure 5-3. Measured Sensitivity Loss Versus Frequency Offset (BW = 165 kHz, ASK, DR = 2.4 kBit/s)

{Δ f}_{\max A S K} = \frac{{B W}_{I F}}{2} - {D R}_{A S K} - \frac{{B W}_{I F}}{2} (58)

Figure 5-4. Measured Sensitivity Loss Versus Frequency Offset (BW = 80 kHz, ASK, DR = 20 kBit/s)

The preceding figure shows the measured and calculated maximum frequency offset derived from equation (57) for low loss in ASK sensitivity. It is advisable to use this for system design.

Table 5-4. Max Frequency Offset for Low Sensitivity Loss Using ASK
Channel Filter Bandwidth	Manchester Data Rate	Recommended Maximum Frequency Offset for Low Loss Based on Measurement	Calculated Frequency Offset with Equation
25 kHz	2.4 kBit/s	±9.6 kHz	±8.5 kHz
25 kHz	5 kBit/s⁽¹⁾	±9.6 kHz⁽¹⁾	±5.9 kHz
80 kHz	2.4 kBit/s	±32.5 kHz	±32.5 kHz
	10 kBit/s	±31 kHz	±25 kHz
	20 kBit/s⁽¹⁾	±31 kHz⁽¹⁾	±15 kHz
165 kHz	2.4 kBit/s	±67 kHz	±69.5 kHz
165 kHz	20 kBit/s	±55.5 kHz	±52.0 kHz
366 kHz	2.4 kBit/s	±157 kHz	±158 kHz
366 kHz	20 kBit/s	±147 kHz	±140 kHz

Note: See the description of the Frequency Offset for 1.5 dB Sensitivity Loss Using an ASK System in the Estimation of Maximum Frequency Offset Between Receiver and Transmitter from Related Links.