Digital-to-Analog Converter (DAC) Output Response TIPL 4705

Presented by Matt Guibord Prepared by Matt Guibord

1 What is a Digital-to-Analog Converter (DAC)?

0x1FF3 0x355A 0x0105 0xF23E 0x5046 0xCC41 0x51F6 0xAB10 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

1 1 Weighted by digital samples 0.5

0 0 Amplitude Amplitude (V) Amplitude

-0.5

-1 -1

0 1 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Normalized Time (t/T) 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 0 0

-20 -10

Weighted by -40

-20 digital samples -60

-30 -80 Power (dBFS) Power Power (dBFS) Power -100 -40

-120

-50 -140

-60 -160 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Normalized Output Frequency (Fout/Fs) Normalized Output Frequency (Fout/Fs)

4 What is a Nyquist Zone? DAC Output - Frequency Domain • A Nyquist zone corresponds to a 0 123456 band of frequencies Fs/2 wide, -20 where F is the DAC’s sampling rate S -40 • Each Nyquist zone is F /2 wide, S -60 starting at DC: – The 1st Nyquist zone extends -80 from DC to F /2 S (dBFS) Power -100 – The 2nd Nyquist zone extends -120 from FS/2 to FS

– And so on… -140 • Note that even Nyquist zones have -160 a mirrored spectrum 0 0.5 1 1.5 2 2.5 3 Normalized Output Frequency (Fout/Fs)

5 Illustration of DAC Output Response

Loss of output power at higher Images in other Nyquist Images result in stair-case response frequencies due to sinc response zones must be filtered out in reconstructed waveform

Desired signal

DAC Output - Sinx/x Response DAC Output - Frequency Domain DAC Output - Time Domain 0 0

123456 123456 1 -5 -20

-10 -40 0.5 -15 -60

-20 -80 0 Power (dBFS) Power Amplitude (V) Amplitude -25 (dBFS) Power -100 -0.5 -30 -120

-35 -140 -1

-40 -160 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Normalized Output Frequency (Fout/Fs) Normalized Output Frequency (Fout/Fs) Time (us)

DAC Sinx/x Response for Zero-Order Hold DAC Frequency Domain for Sine Wave Output DAC Time Domain for Sine Wave Output and Reconstruction Waveform and ZOH Reconstruction Waveform ZOH Reconstruction Waveform

6 Inverse Sinc Filter Inverse Sinc Filter Response • 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 ~80% 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

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 0 “reconstruction filter” 123456 -10 • An example (ideal) 5th-order low-pass Butterworth filter is shown with a cutoff -20 frequency at 80% of the 1st Nyquist zone -30 -40

Power (dBFS) Power -50

-60

-70

-80 0 0.5 1 1.5 2 2.5 3 Normalized Output Frequency (Fout/Fs)

8 Reconstruction Filter Example

•FS = 1 Gsps, FOUT = 30 MHz • Attenuation of 2nd Nyquist zone image = ~40 dB • Stair-case DAC output becomes a smooth sine wave after image removal

DAC Output - Frequency Domain DAC Output - Time Domain

0 DAC Frequency Response Unfiltered DAC Output Reconstruction 1 waveform Filter Response After Reconstruction Filter -20

-40 Reconstruction 0.5 filter -60

Largest undesired 0 -80 image power Amplitude (V)Amplitude Power (dBFS) Power -100 -0.5 -120

-140 -1

-160 0 0.5 1 1.5 2 2.5 3 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Normalized Output Frequency (Fout/Fs) Time (us)

9 Reconstruction Filter Example

•FS = 1 Gsps, FOUT = 400 MHz • Attenuation of 2nd Nyquist zone image = ~18 dB • May want to increase cutoff frequency and increase filter order

DAC Output - Frequency Domain DAC Output - Time Domain

0 Reconstruction waveform DAC Frequency Response Unfiltered DAC Output Reconstruction Filter Response 1 After Reconstruction Filter -20 filter Largest undesired -40 image power 0.5

-60

-80 0 Amplitude (V)Amplitude Power (dBFS) Power -100 -0.5 -120

-140 -1

-160 0 0.5 1 1.5 2 2.5 3 0 0.005 0.01 0.015 0.02 Normalized Output Frequency (Fout/Fs) Time (us)

10 Can we use the image in a different Nyquist zone?

DAC Output - Frequency Domain 0

-20 123456 Reconstruction waveform -40 attenuation

-60

-80

Power (dBFS) Power -100

-120

-140

-160 0 0.5 1 1.5 2 2.5 3 Normalized Output Frequency (Fout/Fs)

11 Multi-Nyquist Modes • The common ZOH reconstruction waveform results in a fairly flat response in the 1st 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) – 1st Nyquist only – Return-to-Zero (RTZ) – 1st and 2nd Nyquist – Return-to-Complement (RTC), also called Mixed Mode or RF Mode –2nd and 3rd • 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

12 Zero-Order Hold (or Non-return to Zero, NRZ)

Reconstruction Waveform Frequency Response

DAC Output Waveform DAC Output - Sinx/x Response 0

1 Loss in 2nd and higher -5 Nyquist zones

-10

-15

0 -20 Amplitude

Power (dBFS) Power -25

-30

-35 -1

-40 0 1 0 0.5 1 1.5 2 2.5 3 Normalized Time (t/T) Normalized Output Frequency (Fout/Fs)

13 Zero-Order Hold (or Non-return to Zero, NRZ)

Time Domain Waveform Frequency Domain

DAC Output - Time Domain DAC Output - Frequency Domain 0

1 -20

-40 0.5 -60

0 -80 Amplitude (V) Amplitude Power (dBFS) Power -100 -0.5 -120

-140 -1

-160 0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.5 1 1.5 2 2.5 3 Time (us) Normalized Output Frequency (Fout/Fs)

14 Return-to-Zero (RTZ)

Reconstruction Waveform Frequency Response

DAC Output Waveform DAC Output - Sinx/x Response 0 6 dB loss in 1st Nyquist 1 -5

-10

Flatter response -15 through 1st and 2nd Nyquist 0 -20 Amplitude

Power (dBFS) Power -25

-30

-35 -1

-40 0 0.5 1 0 0.5 1 1.5 2 2.5 3 Normalized Time (t/T) Normalized Output Frequency (Fout/Fs)

15 Return-to-Zero (RTZ)

Time Domain Waveform Frequency Domain

DAC Output - Time Domain DAC Output - Frequency Domain 0

1 -20

-40 0.5 -60

0 -80 Amplitude (V) Amplitude Power (dBFS) Power -100 -0.5 -120

-140 -1

-160 0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.5 1 1.5 2 2.5 3 Time (us) Normalized Output Frequency (Fout/Fs)

16 Return-to-Complement (RTC) or Mixed Mode

Time Domain Frequency Domain

DAC Output Waveform DAC Output - Sinx/x Response 0 Attenuated 1st Nyquist 1 -5

-10 Enhanced power -15 and flat response through 2nd Nyquist

0 -20 Amplitude

Power (dBFS) Power -25

-30

-35 -1

-40 0 0.5 1 0 0.5 1 1.5 2 2.5 3 Normalized Time (t/T) Normalized Output Frequency (Fout/Fs)

17 Return-to-Complement (RTC) or Mixed Mode

Time Domain Waveform Frequency Domain

DAC Output - Time Domain DAC Output - Frequency Domain 0

1 -20

-40 0.5 -60

0 -80 Amplitude (V) Amplitude Power (dBFS) Power -100 -0.5 -120

-140 -1

-160 0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.5 1 1.5 2 2.5 3 Time (us) Normalized Output Frequency (Fout/Fs)

18 Return-to-Complement with Reset Pulse

Time Domain Frequency Domain

DAC Output Waveform DAC Output - Sinx/x Response 0 No Reset Pulse 1 -5 12.5% Reset Pulse 25% Reset Pulse

-10

-15

0 -20 Amplitude

Power (dBFS) Power -25

-30

-35 -1

-40 0 0.375 0.75 1 0 0.5 1 1.5 2 2.5 3 Normalized Time (t/T) Normalized Output Frequency (Fout/Fs)

21 Return-to-Complement (Mixed Mode)

Time Domain Waveform Frequency Domain

DAC Output - Time Domain DAC Output - Frequency Domain 0

1 -20

-40 0.5 -60

0 -80 Amplitude (V) Amplitude Power (dBFS) Power -100 -0.5 -120

-140 -1

-160 0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.5 1 1.5 2 2.5 3 Time (us) Normalized Output Frequency (Fout/Fs)

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!

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