1. Bandpass Sigma-Delta Modulator Michael Vincent Brian McKinney ECEN5007

2. Wireless Communications • Crowded voice/data frequency bands (think 2.5/3 G cellular and 802.11/Bluetooth wireless) require wide dynamic range front ends and precise IF filtering to receive weak signal with strong interface • Momentum in industry to push A/D conversion as close to antenna as possible to allow most of the process to be done digitally (soft-radio)

3. Bandpass Sigma-Delta Modulator • Direct conversion technique first proposed in 1928, however, this technique leads to an image component folded into the baseband as a result of 90 phase error and path mismatch gain error • Sigma-Delta bandpass approach offers no image problem and the possibility of direct downsampling from IF at frequencies higher than the sampling frequency via the mixing property of the sampling process

4. Bandpass Sigma-Delta Modulator • Song proposed switched capacitor direct quadrature demodulation technique • Double loop bandpass modulator proposed requires same number of op amps as standard double loop lowpass modulator without path mismatch (sampling @ 4x the passband center frequency (fc)) • Identical in structure to low-pass modulator except simple integrator is replaced with a two-delay resonator having a gain of –z^-2/(1+z^-2)

5. Bandpass Sigma-Delta Modulator • Resonator can be realized with two-delay integrators that are time multiplexed between the I and Q channel to avoid path mismatch and save space/power •  Bit stream from modulator is bandpass, I and Q lowpass streams can be obtained in DSP hardware by multiplication by {1,0,-1,0} and {0,1,0,-1} yielding a direct quadrature conversion to dc

8. Fully Differential Op Amp • In order to time multiplex the I and Q channels, the amplifiers inserted into a switched capacitor network. • Fully differential op-amps are used to implement the amplifiers.

9. Basic Fully Differential Op Amp

10. Simulation Setup

11. Transient Analysis (1 MHz input)

12. AC Analysis Corner Frequency: 15MHz Phase Margin: 30°

13. Future Op-Amp Improvements • Performance needs little improvement: • 40dB Gain  Sufficient for simple gain stage • 15 MHz BW  Center frequency of 2 MHz • Replace current sources with cascode or other approach • Implement CMFB stage as switched capacitor network.