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university:tools:pluto:users:amp [25 Apr 2018 17:57] – add some info on S parameters Robin Getz | university:tools:pluto:users:amp [21 Jan 2019 14:13] (current) – [Peak to Average] Robin Getz | ||
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==== Theory of Operation ==== | ==== Theory of Operation ==== | ||
- | In a basic sense, amplifiers can be thought of as a tradeoff between signal gain and signal corruption. | + | In a basic sense, amplifiers can be thought of as a tradeoff between signal gain and signal corruption. |
- | === Biasing | + | ==== Power Supply Rejection Ratio (PSSR) |
+ | |||
+ | If the supply of an amplifier changes, its output should not, but it typically does. If a change of X volts in the supply produces an output voltage change of Y volts, then the PSRR on that supply (referred to the output, RTO) is X/Y. The dimensionless ratio is generally called the power supply rejection ratio (PSRR), and Power Supply Rejection (PSR) if it is expressed in dB. //However, PSRR and PSR are almost always used interchangeably, | ||
+ | |||
+ | PSSR can be expressed as a positive or negative value in dB, depending on whether the PSRR is defined as the power supply change divided by the output voltage change, or vice-versa. There is no accepted standard for this in the industry, and both conventions are in use. | ||
==== Log and dB ==== | ==== Log and dB ==== | ||
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^ Power in mW | Power in dBm | | ^ Power in mW | Power in dBm | | ||
| 0.1 mW | -10 dBm | | | 0.1 mW | -10 dBm | | ||
+ | | 0.3 mW | -5 dBm | | ||
| 1 mW | 0 dBm | | | 1 mW | 0 dBm | | ||
+ | | 3.2 mW | 5 dBm | | ||
| 10 mW | 10 dBm | | | 10 mW | 10 dBm | | ||
+ | | 32 mW | 15 dBm | | ||
| 100 mW | 20 dBm | | | 100 mW | 20 dBm | | ||
+ | | 316 mW | 25 dBm | | ||
A doubling of output power (from 1mW to 2mW) is only +3dBm. A gain of +20dBm, is output power increasing by a factor of 100 times in mW. | A doubling of output power (from 1mW to 2mW) is only +3dBm. A gain of +20dBm, is output power increasing by a factor of 100 times in mW. | ||
==== Peak to Average ==== | ==== Peak to Average ==== | ||
+ | |||
+ | The peak-to-average power ratio (PAPR) is the peak amplitude squared (giving the peak power) divided by the RMS value squared (giving the average power). | ||
+ | |||
+ | < | ||
+ | |||
+ | whether expressed in percent in dB, PAPR is dimensionless quantity. | ||
+ | |||
+ | When dealing with signals and amplifiers, it is the peak that we need to be concerned about, not the average power in the signal. Different types of modulation schemes have different peak to average power, and this needs to be taken into account. | ||
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==== Noise ==== | ==== Noise ==== | ||
+ | Two techniques are typically used for analyzing the noise, but each can be cumbersome. Noise spectral density (NSD) defines the noise power per unit bandwidth. It is represented in mean-square dBm/Hz or dBFS/Hz for ADCs and rms nV/√Hz for amplifiers. This incompatibility in units provides an obstacle to calculating system noise when an amplifier is driving an ADC, or a DAC is driving an amplifier. | ||
+ | |||
+ | Noise figure (NF) is the log ratio of input SNR to the output SNR expressed in decibels. This specification, | ||
==== Distortion ==== | ==== Distortion ==== | ||
+ | |||
+ | When a spectrally pure sinewave passes through an amplifier (or other active device), various harmonic distortion products are produced depending upon the nature and the severity of the non-linearity. However, simply measuring harmonic distortion produced by single tone sinewaves of various frequencies does not give all the information required to evaluate the amplifier' | ||
+ | |||
+ | Intermodulation distortion products are of special interest in the IF and RF area, and a major concern in the design of radio receivers. Rather than simply examining the harmonic distortion or total harmonic distortion (THD) produced by a single tone sinewave input, it is often required to look at the distortion products produced by two tones. | ||
+ | |||
+ | As shown in the figure, two tones f< | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The example shows the second and third order products produced by applying two frequencies, | ||
+ | f< | ||
+ | |||
+ | ^ Order of Mixing | ||
+ | | first order | ||
+ | | second order | < | ||
+ | | third order | ||
+ | |||
+ | The second order products located at f< | ||
+ | far away from the two tones, and may be removed by filtering. The third order products located | ||
+ | at 2f< | ||
+ | |||
+ | Third order IMD products are especially troublesome in multi-channel communications systems | ||
+ | where the channel separation is constant across the frequency band. Third-order IMD products | ||
+ | from large signals (blockers) can mask out smaller signals. | ||
==== Power Supply Limits ==== | ==== Power Supply Limits ==== | ||
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| 15 | 31.6 | 1.257 V | 3.556 V | | | 15 | 31.6 | 1.257 V | 3.556 V | | ||
| 20 | 100 | 2.236 V | 6.324 V | | | 20 | 100 | 2.236 V | 6.324 V | | ||
+ | | 25 | 316 | 3.976 v | 11.246 V | | ||
+ | |||
The question is, how do we get +20dBm (6.324V < | The question is, how do we get +20dBm (6.324V < | ||
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==== S Parameters ==== | ==== S Parameters ==== | ||
- | S-parameters are commonly used to characterize 2-port networks. An S-parameter indicates the amount of power leaving one port of the network, given power entering another (or the same) port of the network. For a two port network (one input, one output), we number the ports 1 and 2, and measure 4 different ratios: | + | [[wp> |
- | ^ Measurement ^ Leaving Port ^ Entering Port ^ | + | ^ Measurement |
- | ^ | + | ^ |
- | ^ | + | ^ |
- | ^ | + | ^ |
- | ^ | + | ^ |
{{ http:// | {{ http:// | ||
- | In the case of S21, the suffix “21” denotes the power leaving port 2, with power delivered to port 1. Note that in the RF world, S-parameters are measured using a 50Ω system. The source impedance driving port 1 must be 50Ω, and the load impedance presented to port 2 must also be 50Ω. | + | In the case of S< |
- | Depending on what you are measuring - each measurement can be more important than another. For example, for an amplifier, | + | Depending on what you are measuring - each measurement can be more important than another. For example, for an amplifier, |
- | S Parameters are normally measured over frequency, as a good amplifier will have a flat gain over frequency. When the gain varies over frequency, it is often called ripple. Ripple is evident once S21 is measured over frequency. | + | S Parameters are normally measured over frequency, as a good amplifier will have a flat gain over frequency. When the gain varies over frequency, it is often called ripple. Ripple is evident once S< |
===== Measurements ===== | ===== Measurements ===== | ||
+ | |||
+ | ==== Signal To Noise Ratio ==== | ||
+ | |||
+ | When we consider the performance of a communication link, in the most basic sense, we are interested in the bandwidth and power of the transmitted signal. Bandwidth is measured from the power spectral density of signal and is also proportional to the bit rate. We define average energy per bit as: | ||
+ | |||
+ | < | ||
+ | |||
+ | where < | ||
+ | |||
+ | < | ||
+ | |||
+ | SNR is commonly expressed in SNR in decibels (dB) and the equation above can be rewritten as: | ||
+ | |||
+ | < | ||
+ | |||
+ | When determining SNR of a signal it is important to understand that signals are band limited unlike noise. | ||
+ | |||
+ | ==== Noise Generation and Power ==== | ||
+ | |||
+ | Calculation of power is a non-trivial exercise in practice and in many situations loosely defined. This is especially true when determining SNR. Let us first consider a unique example where we have scaled exponentials (< | ||
+ | |||
+ | < | ||
+ | r = signal+noise; | ||
+ | % View averaged spectrum | ||
+ | freq = linspace(-bandwidth/ | ||
+ | R = reshape(r, | ||
+ | R = fftshift(fft(R)); | ||
+ | R_mean = mean(abs(R), | ||
+ | plot(freq, | ||
+ | </ | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | |||
+ | An obvious question to ask would be "What is the SNR of these signals?" | ||
+ | |||
+ | Now let us connect this to the theoretical concepts. We know that the power spectral density (PSD) is obtained through a Fourier Transform of a signal' | ||
+ | |||
+ | < | ||
+ | |||
+ | where the autocorrelation of our process or signal < | ||
+ | |||
+ | < | ||
+ | |||
+ | In the case of AWGN this autocorrelation is simply: | ||
+ | |||
+ | < | ||
+ | |||
+ | where < | ||
+ | |||
+ | < | ||
+ | signalpower = sqrt(mean(signal.*conj(signal)))^2; | ||
+ | </ | ||
+ | |||
+ | However, the power unit is a bit tricker to determine. | ||
+ | |||
+ | |||
+ | < | ||
+ | |||
+ | |||
+ | where < | ||
+ | |||
+ | ==== S Parameters ==== | ||
+ | |||
+ | This data was taken on a [[https:// | ||
+ | |||
+ | First we calibrate things with a cable, and connector, to make sure we see what is happening. We expect this to be a flat line, with 0dB of gain. (it is a cable after all). | ||
+ | |||
+ | {{: | ||
+ | |||
+ | Then we can look at the S12 of the amplifier board. Here we can see gain between 2 and 3 GHz, with the flat part being between 2.4 and 2.5 GHz, just like we hope. | ||
+ | |||
+ | {{: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | If we vary the amplitude at a constant frequency, we can see the P1dB point at +5dBm. In order to keep things operating in the linear region, we should make sure not to drive the amplifer board with more than +5dBm. | ||
+ | |||
+ | {{: | ||
+ | |||
+ | ==== Results==== | ||
+ | |||
+ | The yellow line is an antenna, the red line is with the same antenna and the amplifier. You can see the +20dB of transmission at 2.4GHz. | ||
+ | |||
+ | {{: | ||
+ | |||
+ | |||
+ | |||