Why is a balun used on the ADAR2004 evaluation board to convert 100 ohm differential pairs to 50 ohm differential pairs, and can the ADAR2004 eval board be directly connected to the AD9083 eval board using a 50 ohm SMA cable?

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The balun is included on the ADAR2004 evaluation board so that the IF output can be easily observed on a 50 ohm single-ended input spectrum analyzer. If you want to connect the ADAR2004 eval board to the AD9083 eval board, then the baluns from both boards should be removed and the boards should be connected together. Additionally, the ground referenced capacitors in the IFOUT- paths (C24, C25, C26, C27) should also be removed.

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ADAR2004: FAQ