Chen's Learning Note

When amplifiers are cascaded together in order to amplify very weak signals, it is generally the first amplifier in the chain which will have the greatest influence upon the SNR because the noise floor is lowest at that point in the chain. If now we have two amplifier with the same gain but different noise figure, which combination of cascading will have more benefit ?  Assume 10dB gain in each amplifier. One amp with NF = 3dB and the other 6dB. When the 3dB NF amplifier is first in cascade, the total noise figure is 3.62 dB. When the 6dB amplifier is first, the total NF is 6.3dB. The amplifier with less noise figure should be cascaded in the first place. If two amplifiers have the same Noise Figure but different gains, the higher gain amplifier should precede the lower gain amplifier to achieve the best overall Noise figure.

We define the IMRR(Image-Rejection Ratio) as the ratio of wanted factor to unwanted factor due to IQ-mismatch. The wanted factor is K1 , unwanted factor is K2, thus

Fourier Transform of Power Delay Profile is called spaced-frequency correlation function, which describes the spreading of a signal in frequency domain . This also give rise to the importance channel parameter - Coherence Bandwidth.

What is dB ? When a physical quantity , such as power or intensity is measured relative to reference level , it can be expressed in decibels(dB). Decibels is a dimensionless unit . For example, the Signal-To-Noise Ratio can be represent in dB. What is dBm ? dBm stands for an absolute power level , which we can define as 10*log(P/1mW) , where the value of P is power in watts . So P=1mW equals 0 dBm. What is the relation between dBm and dBV ? dBm = dBV - 10log(R) + 30 in a system with resistance R. Assume R = 50 ohm, then the relation between dBm and dBV can be describe as dBV = dBm -13. What is dB digital code word ? Assume we have N bits digital code word, then dB digital code word can be define as the following equation :

An amplifier or a filter will have a non-ideal frequency response , in order to easily describe the noise power effect through the amplifier or a filter, we need a Noise Equivalent Bandwidth.

S-parameters describe the input-output power relationship between 2 ports in an electrical system. Notation : for example , Port 1 and Port 2, S 12  represents the power transferred from Port 2 to Port 1. What is the physical meaning of S 21   = - 10dB ? It means if we have 0dB power is delivered to Port 1, then we only have -10dB of power is received at Port 2. What is the physical meaning of return loss/reflection coefficient ? We denote the return loss as S 11 , which represent how much power is reflected from the Port 1/Antenna 1. For example S 11 = 0dB means that all the power is reflected, nothing is radiated. Base on the former description, we can easily observe from a frequency response plot of |S 11 | to decide which frequency will be efficient, say in 2.5 GHz in the figure above. What is the meaning of VSWR ? Impedance mismatch will induce return loss, and this cause a "reflected voltage wave" , which creates standing wave along the transmission...

For most kinds of ADCs : data rate equals sampling rate ,each input sample converts to one output code. Delta-sigma ADC : acquires many input samples to produce one output code.  Which implies  Delta-sigma sampling algorithm lengthens the acquisition time. In the above figure ,the delta-sigma’s modulator samples and quantize the input signal in a coarse fashion, by producing a one-bit stream of data at a very high rate. Delta-sigma modulator includes an integrator , which has the effect of shaping the quantization noise. The F d value is the corner frequency of the internal digital/decimation filter. One uses F d to define the corner frequency of delta-sigma converter’s external anti-aliasing filter . Observe the figure A and figure B above. The modulator sample rate (Fs) shapes the quantization bandwidth. The data rate (F d ) is always smaller than Fs, as in  Figure A and B . Signals in the i...

Rayleigh fading is a reasonable channel model when there are many objects in the environment that scatter the radio signal before it arrives at the receiver. The central limit theorem holds that, if there is sufficiently much scatter , the channel impulse response will be modeled  as a Gaussian process irrespective of the distribution of the individual components. The Rician K factor, defined as the ratio of signal power in dominant component over the scattered, reflected power , which shows in the below figure  is a easy way to understand the behavior of a short-range wireless channel. Short conclusion :  1.  Rayleigh fading is most applicable when there is no dominant propagation along a line of sight between the transmitter and receiver .  2. Rician fading is used while there is a dominant line of sight . (Which is usually used in short-range wireless channel)

A block moving Average have the following equation : The actual implementation will require : (1) N-tap delay element (2) 1-tap delay element (3) 1 shifter (If N = 2 n ) (4) 2 adder An exponential Average will have the following equation : Alpha value will decide the convergence speed and the weight of the current input signal or data. If the alpha value are smaller then the weight of the current input signal affect less. The actual implementation will require : (1) 1-tap delay element. (2) 2 shifter (If alpha = 2 n ) (3) 1 adder We can easily find out that the Exponential Average are easily to implement than the Moving Average. But if we need to observe the instantaneous change data , the moving average method will be accurate than exponential average method.    

Spread-spectrum clock generation (SSCG) is used in some  synchronous digital system   to reduce the spectral density of the  electromagnetic interference (EMI).   Jitter will cause transmitted bit error Because the generated clock will have variation between 5 GHz ~ 4.97 GHz, thus in the time domain , the clock waveform will have time variation. If the variation is too much, then the received waveform will have certain error because of clock timing variation which can be founded in the following figure :

Suppose we want to have a function to deal with a global matrix (@matrix) to do column swap, then we can declare the  function  as following : sub ColSwap {     my ($Idx1,$Idx2) = @_;  # Idx1 and Idx2 are global variable     my ($idx, $Tmp0);       # idx and Tmp0 are local variable , only exist in this function     for ($idx = 0; $idx < $max_col; $idx++)     {            $Tmp0 = $matrix[$Idx1*$max_col + $idx];            $matrix[$Idx1*$max_col + $idx] = $matrix[$Idx2*$max_col + $idx];            $matrix[$Idx2*$max_col + $idx] = $Tmp0;     } } NOTE : matrix and max_col are global variable , we don't need to give any input argument to ColSwap. We can use this kind of function using  &ColSwap (Column#1 , Column#2); We can return value like we  program  in C , for example : s...

1. How to do summation over arbitrary index values within an array ? For example , an array A with 54 elements , we want to have a summation of index 5, 9 ,32 51 , how can we do that ? sum(A([5,9,32,51])) will return what we want , and A can be complex or real. 2. How to do easy sliding conjugate multiplication within an array ? For example , an complex array A with 54 elements , we want to find the sliding conjugate multiplication like A(2) x A(1)* , A(3) x A(2)* ... etc A(2:54).*conj(A(1:53)) will return what we want 3. How to represent an array with known sub-array ? For example , an complex sub-array b , we want a array A = [b b b b b b b b ....] with 50 b elements How can we do this in simple way ? A = repmat(b,1,50) can get what we want in easy way. 4. Radians to Degree radtodeg(a)

1. How to print all the sub-folder names into a file ?    dir/ad/b > file_list.txt    => this will print the subfolder names into file_list.txt 2. How to execute the same batch file in the sub-folders?    for example : xyz.bat      for /d %%a in (*) do (     cd %%a // go to the sub folder     call xyz.bat     cd ..  // back to the folder )

There exist a equation to approximate the complex number x = I + j*Q   Mag ~= Alpha * max(|I|, |Q|) + Beta * min(|I|, |Q|) , but what value of Alpha and Beta should we choose to approximate the best ? 新增說明文字 We actually will focus on RMS approximation error and Peak error, if we focus on RMS error only, then Beta value choose to be ¼ will be good, but the ¼ case Peak error performance are too bad. And Beta choose to be 11/32 will be the best approximation. But this case will be not easy to implement in hardware design. è Therefore we choose 3/8 as the Beta. Which finally we will choose (1, 3/8) as the magic number for approximation.

1. BT Radio Interface With many other users on the ISM band from microwave ovens to Wi-Fi, the hopping carrier enables interference to be avoided by BT devices. A BT transmission only remains on a given frequency for a short time, and if any interference is present the data will be re-sent later when the signal has changed to a different channel which is likely to be clear of other interfering signals. The standard uses a hopping rate of 1600 hops /second, and the system hops over all the available frequencies using a pre-determined pseudo-random hop sequence based upon the BT address of the master node in the network. } During the development of the BT standard it was decided to adopt the use of frequency hopping system rather than a direct sequence spread spectrum approach because it is able to operate over a greater dynamic range. } If direct sequence spread spectrum techniques were used then other transmitters nearer to the receiver would block the required transmission if ...