Method and apparatus for bandpass digital to analog converter

1. A digital to analog converter (DAC) system comprising:

a) a first DAC having a sample input, a clock input and an output, wherein a first stream of samples is provided to the sample input, the first stream of samples being used to set an output level at the output of the first DAC based upon the value of the sample and at a time indicated by a sample clock signal having a sample frequency, fs, the sample clock signal being applied to the clock input, the first stream of samples having a sample time coincident with the timing of the sample clock;

b) a first up-converter having a signal input, a local oscillator (LO) input and a radio frequency (RF) output, wherein the same sample clock signal applied to the clock input of the first DAC is applied to the LO input of the up-converter and the output of the DAC is applied to the signal input of the first up-converter;

c) a second DAC having a sample input, a clock input and an output, wherein a second stream of samples is provided to the sample input of the second DAC, the second stream of samples having a sample time coincident with the timing of a second sample clock signal having the same sample frequency, fs as the first sample clock signal, the second sample clock signal being applied to the clock input of the second DAC, the second sample clock signal having a quadrature offset in time from the first sample clock signal; and

d) a second up-converter having a signal input, an La input and an RF output, wherein the same sample clock signal applied to the clock input of the second DAC is applied to the LO input of the second up-converter and the output of the second DAC is applied to the signal input of the second up-converter.

2. The DAC system of claim 1 , wherein the quadrature offset of the second sample clock signal from the first sample clock signal is −90 degrees.

3. The DAC system of claim 1 , further comprising a digital signal processor, wherein the digital signal processor aligns the sample stream to be provided to the first and second DAC, performs a phase shifting transform (PST) upon the second sample stream, and provides the aligned first sample stream and the aligned and transformed second sample stream to the inputs of the first and second DACs.

4. The DAC system of claim 1 , wherein the PST transforms a baseband signal by phase shifting each of the positive spectral components of the baseband signal by −90 degrees and each of the negative spectral components by 90 degrees with respect to the frequency of each spectral component.

5. The DAC system of claim 1 , wherein the frequency of the LO signals provided to the first and second up-converters are a harmonic of the sample frequency.

6. An full circle N-array DAC system comprising:

a) a plurality of channels comprising:

i) a DAC having a sample input, a clock input, and an output, and receiving a sample stream at the sample input and a sample clock signal having a sample clock frequency, f s at the clock input, the timing of the samples of the stream and the timing of the sample clock signal being coincident; and

ii) an up-converter having a signal input, an LO input and an output; wherein: (1) the number of channels is equal to N; (2) each channel and the associated DAC and up-converter are indexed by the index i, where i has an integer value from zero to N−1, (3) each of the plurality of DACs being provided a sample stream, each sample stream having been transformed by a phase shifting transform using a phase of θ°=−i360/N, the sample time of each sample stream is delayed by τi =iT s /N, where T s =1/f s , each sample clock signal being delayed by τ i , and each up-converter receiving an LO signal at the LO input, the LO signal having a frequency of f s and delayed by τ i .

7. The full circle N-array DAC system of claim 6 , further including a summer for summing the outputs of each channel.

8. The full circle N-array DAC system of claim 6 , wherein the LO signals are delayed by iT s /N.

9. The full circle N-array DAC system of claim 6 , wherein the angle used by the PST to transform the sample streams is i360IN.

10. The full circle N-array DAC system of claim 6 , wherein the delay τ i of the sample clock signal is −iT s /N and the sample time of each sample of the sample stream is delayed by τ i .

11. The half circle N-array DAC system of claim 6 , wherein the LO signals are delayed by iT s /N.

12. The half circle N-array DAC system of claim 6 , wherein the angle used by the PST to transform the sample streams is i360/N.

13. The half circle N-array DAC system of claim 6 , wherein the delay τ i of the sample clock signal is −iT s /N and the sample time of each sample of the sample stream is delayed by τ i .

14. An half circle N-array DAC system comprising:

a) a plurality of channels comprising:

i) a DAC having a sample input, a clock input, and an output, and receiving a sample stream at the sample input and a sample clock signal having a sample clock frequency, f s at the clock input, the timing of the samples of the stream and the timing of the sample clock signal being coincident; and

ii) an up-converter having a signal input, an LO input and an output;

wherein: (1) the number of channels is equal to N; (2) each channel and the associated DAC and up-converter are indexed by the index i, where i has an integer value from zero to N−1, (3) each of the plurality of DACs being provided a sample stream, each sample stream having been transformed by a PST using a phase of θ°=−i360/N, the sample time of each sample stream is delayed by τi =iT s /2N, where T s =1/f s , each sample clock signal being delayed by τ i , and each up-converter receiving an LO signal at the LO input, the LO signal having a frequency of f s and delayed by τ i .