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# RF System Cascade Budget Calculation (*)

For the purpose of this example we will assume that a receiver is required which will translate a 915 MHz digital signal down to baseband with no inversion from input to output. The input covers a 10 MHz band that is divided into 200 kHz sub-bands. A dual conversion will be employed to translate an input signal at 915 MHz down to a 10.7 MHz baseband. A 10 MHz wide downconverter will translate the entire input band to a first IF (intermediate frequency) of 115 MHz. Next, a 200 kHz wide receiver card will translate a 200 kHz section of the 10 MHz band down to 10.7 MHz -- where the information is detected.

Once input and output parameters required for the conversion system are known, the selection of cascaded parameters for each stage in the example are determined. Partitioning of cascaded parameters between the two stages is based on characteristics of available components. Low noise figure requires that a substantial amount of gain be present as close to the input (front end) as possible. High intercept points (and, desirably, good spurious product performance) requires as little gain at the system front end as possible. Balancing the two requirements for optimal performance can be the designer's biggest challenge. As an example, consider the following system where there are two gain stages. Both systems are identical with the exception of gain distribution - although the total gain remains constant. The parameters listed above the components are valid at the component output.

The system of Figure 1 has low gain at the front end, while the system of Figure 2 has high gain at the front end. For cascade equations, see IP2, IP3, and NF pages on RF Cafe. Gain for uncompressed stages is a simple addition.

Figure 1    System With Low Input Gain

Figure 2    System With High Input Gain

Cascaded calculations were carried out to determine the values at the system output, and then the equivalent input parameters were calculated. Both systems have a total of +30 dB gain. Compare the resulting cascaded parameters at the system input to realize the effects of gain distribution. Whereas the system with low front end gain has the best intercept point performance, the system with high front end gain has the best noise figure performance.

Figure 3 shows the Planning screen created for the two conversion stages. I/O specifications are imposed allowing TxRx Designer to determine the minimum requirements for each stage. Load EXAMPLE.PF3 while on the Planning screen to view the plan.

Figure 3    Example Planning Screen

Each stage is designed individually to conform to the stage 1 and stage 2 requirements. A swept input is used during the design of each stage with input parameters set at default values so as not to affect the system output parameters (gain = 0 dB, P1dB = +250 dBm, etc.). Figure 4 and Figure 5 represent the two system stages shown in Figure 3.

Figure4    Example Stage 1

Figure 5    Example Stage 2

Parameters used for each stage in this example are specified to exactly match the values determined by TxRx Designer on the Planning screen as a testimony to the accuracy of the calculations when the two stages are combined. In practice, each stage will most likely perform better than the minimum requirements.

Launch the TxRxD v3.0 Stage 1 and TxRxD v3.0 Stage 2 PIF files. Load EXST1.SF3 into TxRxD v3.0 Stage 1 and EXST2.SF3 into TxRxD v3.0 Stage 2. Immediately after loading each file, select Restore Last Scale from the Graph menu and toggle Auto Scale to Manual. Verify that the systems match the ones shown in Figure 4 and Figure 5.

Switch to TxRxD v3.0 Stage 1 and set INPUT to sweep through 1 MHz in 10 kHz steps. After recalculation, save the system file in order to create a data file (EXST1.DF3) that TxRxD v3.0 Stage 2 can read as input data.

Switch to TxRxD v3.0 Stage 2 and select Switch to Data File Input... from the Components menu (EXST1.DF3 is already specified as the input file). Select Restore Last Scale from the Graph menu. The system of Figure 6 will result.

Figure 6    Example Stage 2 with Stage 1 Input Data

The final output cascaded parameters match with the output parameters specified on the Planning screen. Note that the noise figure is slightly less than the targeted 5.0000 dB due to the internal accuracy of TxRx Designer being much greater than the five place displayed accuracy. Three ten thousandths of a decibel is insignificant.

A close inspection of the frequency responses of Figure 5 (swept input) and Figure 6 (stage 1 data file input) will reveal the effect of the stage 1 contributions to amplitude and group delay. The additive effects of the group delay are most apparent.

* Excerpted from the user's manual from TxRx Designer (now RF Workbench).