ETIN55 Integrerade A/D och D/A omvandlare
This is an errata list for the course book. Please report suspected errors to the course representatives to make the list more complete.
[Data Converters], p.19, equation 1.16
Problem: Wrong symbol
Solution: Psine should be Ptrian
[Data Converters], p.20, equation 1.21
Problem: Equation 1.21 is completely wrong, and probably not the one used to generate figure 1.16.
Solution: The correct expression for the ENB can be found in the lecture slides.
[Data Converters], p.23, equation 1.25
Problem: The integrand of the inner integral in Equation 1.25 is wrong.
Solution: It should be the voltage squared given by Equation 1.24.
[Data Converters], p.24, Fig. 1.19
Problem: y-axis is wrong
Solution: It should be sqrt(kT/C), and not kT/C
[Data Converters], p.28, in the text
Problem: ...coherent sampling for which an integer number of clock cycles, k, fits into the sampling window...
Solution: ...coherent sampling for which an integer number of signal periods, k, fits into the sampling window...
[Data Converters], p.35, equation1.40
Problem: wrong expression of HS&H
Solution: romeve the leading "j" in the expression
[Data Converters], p.42, equation 1.55 and 1.56
Problem: The equations and texts do not correspond
Solution: Equation 1.55 is the backward transformation, while 1.56 is the forward transformation and not the other way around.
[Data Converters], p.57, the second paragraph of the text
Problem: Reference to equation 2.2 is wrong.
Solution: The correct reference should be to equation 2.1
[Data Converters], p.57, figure 2.8
Problem: Even though the text in the last paragraph about the DNL/INL talks about the running sum of the correlated part of the DNL, figure 2.8 is referring to the correlated INL.
Solution: Swapping INL for DNL in figure 2.8 makes more sense.
[Data Converters], p.57, equation 2.3
Problem: This equation for transition points after correction (for gain and offset) X'(k) does not make sense. Setting kos=0 and all DNLs=0 gives that all transition points should be X'(k)=0 for all k.
Solution: Better equations for DNL and INL are presented in the lecture slides.
[Data Converters], p.58, example 2.1
Problem: Implementing equation 2.5 with the described values does not generate the plots in figure 2.9 and 2.10.
Solution: The MATLAB code has a factor 800 multiplied to the equation for y. This factor is missing in the example text.
[Data Converters], p.59, example 2.1, in the figures
Problem: Figure 2.9 and 2.10 are probably not the correct figures for this example
Solution: The output spectrum should contain the 2nd, 3rd and 4th order harmonic tones of the input tone since both a=-0.01, b=0.01 and c=0.02 are set in the polynomial describing the nonlinearity. The reason for this problem is that in the MATLAB code an 11 bit quantization is implemented rather than a 12 bit quantization like it says in the example. A division by 2^(N-1) is done rather than by 2^N in the code, so the harmonics drown in quantization noise.
[Data Converters], p.68-69
Problem: Two-tone intermodulation distortion is given the acronym IMD2; however, IM2 (IM3) is commonly used to indicate the second-order (third-order) intermodulation distortion, i.e., the distortion caused by a quadratic (cubic) non linearity in the transfer function.
Solution: Be aware of the above.
[Data Converters], p.71
Problem: In the definition of ERBW, it is not clear whether the amplitude of the input signal is arbitrary or not.
[Data Converters], p.119, equation 3.29.
Problem: Equation error
Solution: The equation shall be multiplied by 1/2 to be correct.
[Data Converters], p.120, equation 3.34.
Problem: Equation error
Solution: Caused by using the erroneous result from 3.29.
[Data Converters], p.143, section 4.2, 2nd paragraph
Problem: 1/2 LSB = Vfs/(2^n+1)
Solution: Should be 1/2 LSB = Vfs/(2^(n+1))
[Data Converters], p.144, eqs. 4.8-4.9
Problem: Equation errors
Solution: In 4.8, "erf" should be replaced with "erfc". Furthermore, 4.9 is an expression of the time constant T_C, and not of the delay T_D (see Kaupp, JSSC Aug. 1989, cited in p. 207).
[Data Converters], p.145-146, example 4.2, calculation error
Problem: The final calculation of the jitters is wrong
Solution: The noise should be divided by the slope to get 41 fs and 14 fs.
[Data Converters], p.148, equation 4.13
Problem: Equation error.
Solution: In the equation, it looks like Vref- is multiplied by the rest of the equation. Actually, there should be an addition (+ sign) between Vref- and the rest.
[Data Converters], p.156, equation 4.20
Problem: The equation results in to low current (80 uA).
Solution: The expression for the bias current should be multiplied by the dynamic gain A0. Thus the correct answer should be 1.6 mA. For the 7-bit converter the current would be 204.8 mA.
[Data Converters], p.160, second paragraph of the text.
Problem: Reference to fig 4.12
Solution: Should be a reference to fig. 4.11.
[Data Converters], p.169, Fig. 42(b).
Problem: Curve Vo(i+1)
Solution: Should have zero-crossing at Vref(i+1)
[Data Converters], p.172, equation 4.28 and figure 4.24
Problem: Errors in the equation
Solution: The eout,i in the figure is called eI,i in the equation. Furthermore, the multiplication Rout*RT,i should be a division Rout/RT,i.
[Data Converters], p.176, 6 lines after equation 4.32
Problem: Images are said to be located at k*f_s/(2N) +- f_in
Solution: Images are located at k*f_s/N +- f_in
[Data Converters], p.180, figure 4.30
Problem: The sampled and held voltage does not correspond to the output code, even in the example with the correct ouput code.
Solution: The correct S&H voltage should be 0.4296875.
[Data Converters], p.186, figure 4.35
Problem and solution: The bits in the second stage og the pipeline converter at time n+1 should be b7-b6, not b9-b8.
[Data Converters], p.217, in the text
Problem: Notations in the figure and text mismatch.
Solution: IB1 in the text refers to I1 in the figure and IB2 in the text refers to I2 in the figure.
[Data Converters], p.218, equation 5.6.
Problem: An error in the equation.
Solution: The dVin should be divided by dt, not by a comma!
[Data Converters], p.219, figure 5.9.
Problem: The figure is empty.
Solution: Run the MATLAB file Ex5_1.m to get the figure.
[Data Converters], p.220, equation 5.10
Problem: The noise coefficient gamma should not be 2/3 for a bipolar transistor.
Solution: The gamma for bipolar transistors are typically 1/2, 2/3 is valid in the ideal case for a MOS transistor.
[Data Converters], p.220, in the fourth paragraph of the text
Problem: It is claimed that the small signal output impedance of the current source will generate noise, which is a fundamental mistake.
Solution: It is a well known fact that small signal parameters do not generate any noise.
[Data Converters], p.221, equation 5.12
Problem: The noise coefficient gamma is used as a noise excess factor.
Solution: The gamma of equation 5.12 is not the same as the gamma of equation 5.11, in the lecture slides we have denoted this excess noise factor gamma'.
[Data Converters], p.231, in the last paragraph of the text
Problem: The conclusion for the noise from generator (3) in Fig. 5.18 is wrong. Solution: The noise sampling on the two capacitors does not cancel the noise from generator (3). Rather on the contrary, the noise is actually amplified by 2.
[Data Converters], p.235, figure 5.20
Problem: The arrows in the picture point to nothing.
Solution: The pictures are corrected in the lecture slides.
[Data Converters], p.236, equation 5.26
Problem: Error in the equation.
Solution: Instead of Vin-Vthp it should be Vin-|Vthp|.
[Data Converters], p.239, in the first paragraph of the text.
Problem: The reason for the bootstrapping is not properly explained.
Solution: Since the gate-source voltage of the switch is almost independent of the input voltage Vin, the linearity of the switch is greatly improved.
[Data Converters], p.239, figure 5.24.
Problem: The schematic has an error
Solution: The gate of M1 should be connected to the gate of Md2 (source of Md1) for this circuit to work properly.
[Data Converters], p.240, in the text, paragraph 3.
Problem: The reason for not using a PMOS transistor is not clearly explained.
Solution: The reason is that with a PMOS transistor, Vg of M1 would need to become larger than Vdd during the switch on-phase. To avoid that, a more complex biasing scheme would be needed.
[Data Converters], p.243, section 5.8, third sentence
Problem: The operation regions of the transistor has been mixed up.
Solution: "As a matter of fact, a MOS transistor in the saturation region....
[Data Converters], p.246, figure 5.28
Problem: The figure is not referred to anywhere in the text.
Solution: The figure belongs to example 5.4. It shows the transconductance of the V-I converter, with the input voltage on the y-axis and the output current on the x-axis.
[Data Converters], p.255, figure 6.2.
Problem: The (a) figure is unclear.
Solution: What looks like a buffer in the figure is meant to be an integrator. There should be some integrator sign on the buffer in the feedback path.
[Data Converters], p.256, figure 6.3.
Problem: The (a) and (b) figures are unclear.
Solution: What looks like buffers in the figures are meant to be integrators. There should be some integrator sign on the buffers in the forward path.
[Data Converters], p.257, paragraph 3, sentence 3.
Problem: The blocks have been mixed up in the text.
Solution: "A second processing block B(z)...
[Data Converters], p.260, paragraph 3.
Problem: An error in the text
Solution: "..., the number of bits sent to the digital filter is the upwards rounding of log2(k+1) ;therefore, ..."
[Data Converters], p.260-262, example 6.1.
Problem: With Vfs=1V, the input signal with amplitude 0.85 V would cause overload of the quantizer of the Delta-Sigma ADC.
Solution: In the simulation leading to the results in figure 6.8, Vfs=2V was used, so clipping was avoided. However, that makes the calculation of the quantization noise power and PSD of the quantization noise close to f=fs/2 wrong. They should be recalculated with delta=1/4.
[Data Converters], p.265, paragraph 2, sentence 2.
Problem: Strange choice of words using dump instead of damp.
Solution: "..., it is necessary to damp one of the two integrators..."
[Data Converters], p.268, equation 6.26.
Problem: C1 [... Vout(nT)/A0].
Solution: C1 [... Vout(nT+T)/A0].
[Data Converters], p.272-273, in the text.
Problem: Different notations have been used for the same thing.
Solution: Vstep and DVout is probably the same thing, and t and td is also the same thing.
[Data Converters], p.274, in the text and figure 6.17.
Problem: The SR limitation is not the same in the text as in the figure.
[Data Converters], p.276, equation 6.41.
Problem: The equation does not tale into account that the quantization noise is shaped.
Solution: The r.h.s of the inequality is given by the shaled noise power in eq. 6.23 (in the case of a 2nd order modulator).
[Data Converters], p.360, figure 8.1.
Problem: The reference voltage connected to C1 and C2 is called VB in the text, but Vref in the figure. There is also a reference to Vdac in the text, not shown in any figure.
Solution: The notation in the figure is wrong since Vref is used to denote the DAC voltage. Probably Vdac is the same as Vref.
[Data Converters], p.363, equation 8.5 and 8.6.
Problem: There are two different notations for Vref, Vdac and Vref.
Solution: It should be Vref in equation 8.6 instead of Vdac.
[Data Converters], p.370, equation 8.9.
Problem: Error in the equation.
Solution: Where it says dG,i it should probably be (1+dG,i).
[Data Converters], p.374, equation 8.13.
Problem: It is a bit unclear how to arrive at equation 8.13. At least, it seems like the fact stated in the text, X1+X2=1 is not used.
[Data Converters], p.379, equation 8.20.
Problem: Error in the equation.
Solution: Firstly, the power of the full scale sine wave, mentioned in the text should be (M*X)^2/8. That makes equation 8.20 wrong. Secondly, the OSR should be in the nominator of the SNR expression, so that the SNR increases when OSR increases.
[Data Converters], p.383, fig. 8.22.
Problem: The plots for elements #4 and #6 in (a) (rotation approach) are wrong.
[Data Converters], p.387, in the text.
Problem: "...the total error given by of the elements..."
Solution: "...the total error given by the elements..." or "...the total error of the elements..."