Digital-to-Analog Converter (DAC) Output Response TIPL 475 Presented by Matt Guibord Prepared by Matt Guibord
What is a Digital-to-Analog Converter (DAC)? xff3 x355a x5 xf23e x546 xcc4 x5f6 xab Reconstruction Waveform 2
Reconstruction Waveform Time Domain A reconstruction waveform determines the output response of a DAC, in both time domain and frequency domain At each sampling instance the DAC outputs the waveform weighted by the digital sample DAC Output Waveform DAC Output - Time Domain Amplitude Weighted by digital samples Amplitude (V).5 -.5 - - Normalized Time (t/t).5..5.2.25.3.35 Time (us) 3
Reconstruction Waveform Frequency Domain The shape of the reconstruction waveform results in a certain frequency response The frequency response determines the output power of the desired signal as well as the power of some undesired signals DAC Output - Sinx/x Response DAC Output - Frequency Domain - -2-3 -4-5 Weighted by digital samples -2-4 -6-8 - -2-4 -6.5.5 2 2.5 3-6.5.5 2 2.5 3 4
What is a Nyquist Zone? A Nyquist zone corresponds to a band of frequencies Fs/2 wide, where F S is the DAC s sampling rate Each Nyquist zone is F S /2 wide, starting at DC: The st Nyquist zone extends from DC to F S /2 The 2 nd Nyquist zone extends from F S /2 to F S And so on Note that even Nyquist zones have a mirrored spectrum -2-4 -6-8 - -2-4 DAC Output - Frequency Domain 2 3 4 5 6-6.5.5 2 2.5 3 5
Illustration of DAC Output Response Loss of output power at higher frequencies due to sinc response Desired signal Images in other Nyquist zones must be filtered out Images result in stair-case response in reconstructed waveform -5 DAC Output - Sinx/x Response 2 3 4 5 6-2 DAC Output - Frequency Domain 2 3 4 5 6 DAC Output - Time Domain - -4.5-5 -2-25 -6-8 - Amplitude (V) -3-2 -.5-35 -4 - -4.5.5 2 2.5 3 DAC Sinx/x Response for Zero-Order Hold Reconstruction Waveform -6.5.5 2 2.5 3 DAC Frequency Domain for Sine Wave Output and ZOH Reconstruction Waveform.5..5.2.25.3.35 Time (us) DAC Time Domain for Sine Wave Output and ZOH Reconstruction Waveform 6
Inverse Sinc Filter A simple method used to recover the output power loss due to the sinc response is to use a digital filter to apply gain at higher frequencies This example filter flattens the output response through ~8% of the Nyquist zone Care must be taken to ensure that the applied gain does not cause saturation of the digital path for full scale signals Inverse Sinc Filter Response 7
Reconstruction Filter An analog filter is required at the output of the DAC to select the desired image signal and attenuate the undesired images This analog filter is called a Reconstruction Filter Response reconstruction filter - 2 3 4 5 6 An example (ideal) 5 th -order low-pass -2 Butterworth filter is shown with a cutoff frequency at 8% of the st Nyquist zone -3-4 -5-6 -7-8.5.5 2 2.5 3 8
Reconstruction Filter Example F S = Gsps, F OUT = 3 MHz Attenuation of 2 nd Nyquist zone image = ~4 db Stair-case DAC output becomes a smooth sine wave after image removal DAC Output - Frequency Domain DAC Output - Time Domain -2 Reconstruction waveform DAC Frequency Response Filter Response Unfiltered DAC Output After Reconstruction Filter -4-6 -8 - -2 Reconstruction filter Largest undesired image power Amplitude (V).5 -.5-4 - -6.5.5 2 2.5 3.5..5.2.25.3.35 Time (us) 9
Reconstruction Filter Example F S = Gsps, F OUT = 4 MHz Attenuation of 2 nd Nyquist zone image = ~8 db May want to increase cutoff frequency and increase filter order -2-4 DAC Output - Frequency Domain Reconstruction waveform Reconstruction filter DAC Frequency Response Filter Response Largest undesired image power.5 DAC Output - Time Domain Unfiltered DAC Output After Reconstruction Filter -6-8 - -2 Amplitude (V) -.5-4 - -6.5.5 2 2.5 3.5..5.2 Time (us)
Can we use the image in a different Nyquist zone? -2-4 DAC Output - Frequency Domain 2 3 4 5 6 Reconstruction waveform attenuation -6-8 - -2-4 -6.5.5 2 2.5 3
Multi-Nyquist Modes The common ZOH reconstruction waveform results in a fairly flat response in the st Nyquist zone, but suffers from high loss in higher Nyquist zones If an alternate Nyquist zone image is desired, then a different reconstruction waveform should be used Common reconstruction waveforms: Zero-Order Hold (ZOH) or Non-Return-to-Zero (NRZ) st Nyquist only Return-to-Zero (RTZ) st and 2 nd Nyquist Return-to-Complement (RTC), also called Mixed Mode or RF Mode 2 nd and 3 rd Adjustable reset pulses can also be added to these waveforms to further enhance high frequency output power and flatness The reconstruction waveform is a tradeoff of output power and flatness 2
Zero-Order Hold (or Non-return to Zero, NRZ) Reconstruction Waveform DAC Output Waveform Frequency Response DAC Output - Sinx/x Response -5 - Loss in 2 nd and higher Nyquist zones Amplitude -5-2 -25-3 - -35 Normalized Time (t/t) -4.5.5 2 2.5 3 3
Zero-Order Hold (or Non-return to Zero, NRZ) Time Domain Waveform DAC Output - Time Domain Frequency Domain DAC Output - Frequency Domain -2 Amplitude (V).5 -.5-4 -6-8 - -2 -.5..5.2.25.3 Time (us) -4-6.5.5 2 2.5 3 4
Return-to-Zero (RTZ) Reconstruction Waveform DAC Output Waveform Frequency Response DAC Output - Sinx/x Response 6 db loss in st Nyquist -5 - Amplitude -5-2 -25 Flatter response through st and 2 nd Nyquist -3 - -35.5 Normalized Time (t/t) -4.5.5 2 2.5 3 5
Return-to-Zero (RTZ) Time Domain Waveform DAC Output - Time Domain Frequency Domain DAC Output - Frequency Domain -2 Amplitude (V).5 -.5-4 -6-8 - -2 -.5..5.2.25.3 Time (us) -4-6.5.5 2 2.5 3 6
Return-to-Complement (RTC) or Mixed Mode Time Domain DAC Output Waveform Frequency Domain DAC Output - Sinx/x Response Attenuated st Nyquist -5 - Amplitude -5-2 -25 Enhanced power and flat response through 2 nd Nyquist -3 - -35.5 Normalized Time (t/t) -4.5.5 2 2.5 3 7
Return-to-Complement (RTC) or Mixed Mode Time Domain Waveform DAC Output - Time Domain Frequency Domain DAC Output - Frequency Domain -2 Amplitude (V).5 -.5-4 -6-8 - -2 -.5..5.2.25.3 Time (us) -4-6.5.5 2 2.5 3 8
Return-to-Complement with Reset Pulse Time Domain DAC Output Waveform Frequency Domain -5 DAC Output - Sinx/x Response No Reset Pulse 2.5% Reset Pulse 25% Reset Pulse - Amplitude -5-2 -25-3 - -35.375.75 Normalized Time (t/t) -4.5.5 2 2.5 3 2
Return-to-Complement (Mixed Mode) Time Domain Waveform DAC Output - Time Domain Frequency Domain DAC Output - Frequency Domain -2 Amplitude (V).5 -.5-4 -6-8 - -2 -.5..5.2.25.3 Time (us) -4-6.5.5 2 2.5 3 22
Effect of Limited Output Bandwidth The effect of the reconstruction waveform and reconstruction filters and their effect on output power of desired and undesired signals has been discussed One additional consideration is the effect of finite output bandwidth of the DAC or external components Consider the passive losses of the DAC, not including the reconstruction waveform contributions Additional losses may come from passive components (resistors, capacitors, inductors), PCB trace losses and transformer or balun losses The attenuation of these components add (in db) to the reconstruction waveform and reconstruction filter responses to get the total output frequency response of the DAC and signal chain 23
Thanks for your time! 24
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