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Amplifiers

In this article, we will examine the basics of propagation and motivate the use of amplifiers for RF transmission. We will also discuss some important specifications of amplifiers that are typically approached by practicing engineers.

Transmission

To understand power in RF transmission, we need to go back to high school physics and do a little thought experiment.

Imagine a Dyson Sphere, an artificial hollow sphere of matter around a star. The energy (in Joules) that the encompassed star provides spreads out uniformly in all directions. The Luminosity or Power the star puts out is based on Joules/second, or Watts. The Brightness or power received at the surface of the Dyson-sphere received is based on the distance from the star and the surface of the inner surface of the sphere (and is measured in Watts/m^2). Suppose the Dyson-sphere has a radius of r, then the surface area of that sphere is $4{pi}r^2$ .

If the total output power (or Luminosity) of the star is L Watts, and the surface area of that sphere is $4{pi}r^2$ , So the energy flowing through each square meter of the sphere every second is:

$B = L/{4{pi}r^2}$

We call that the star’s brightness, B, and is measured in Watts/meter^2. This is known as a form of the “Inverse Square Law”, as the relationship is $1/{r^2}$ not

If the distance, r, is doubled then the brightness, B, (or received brightness) decreases by a factor of $1/{2^2}$ or a quarter the brightness.

If the distance, r, is tripled then the brightness, B, (or received brightness) decreases by a factor of $1/{2^3}$ or a eighth the brightness.

You can also look at this from the opposite way - if you need to read a book on the surface of the Dyson-sphere, what kind of output power do you need from the star, to get the appropriate amount of brightness? To double the brightness, you need to increase the power of the star by 4 times.

If you still are not sure lets go way back to the middle school butter gun analogy, by watching the excellent video, put together by Roger Linsell of http://www.fizzics.org/.

Free Space Path Loss

As energy is transmitted by any transceiver it becomes dispersed across space and absorbed by the surrounding environment. This is typically referred to as path loss or loss or attenuation of energy over a distance. Although generally not accurate in most situations, the most common model for path loss is free-space path loss (FSPL). FSPL is the energy loss in an obstacle-free, line-of-sight path through free space. FSPL is proportional to the square of the distance:

$L=({4 pi d}/lambda)^2 = ({4 pi d f}/c)^2$ ,

where is the distance (meters) from the transmitter, is the signal or carrier frequency (hertz), is the wavelength (meters), and is the speed of light (meters per second). The equation above also assumes the transmitter is isotropic and is measured from the far field.

This equation is typically provided in which can be calculated as:

$L_{dB}=10log_10(({4 pi d f}/c)^2) = 20log_10(({4 pi d f}/c)) = 20log_10(d) + 20log_10(f) + 20log_10({4 pi}/c)$ .

Let us get some perspective on this equation from looking at the idea of receiver sensitivity (RS), which is the minimum power a signal can be received at and still recovered. For WiFi 802.11ac, this requirement is [FIX ME and ref]. Operating at and examining distance as a function of transmit power we can observe the limited range of Pluto alone in orange in the figure below. However, by adding a amplifier to Pluto we can substantially increase its range.

Practical things

Theory of Operation

In a basic sense, amplifiers can be thought of as a tradeoff between signal gain and signal corruption. Gain is simply the ratio of the input to output signal amplitude. However, signal corrupt comes fin many forms but usually categorized as noise and distortion.

Power Supply Rejection Ratio (PSSR)

Log and dB

The power P_dBm in dBm is equal to 10 times the base 10 logarithm of the power P_mW in milliwatts (mW) divided by 1 milliwatt (mW):

$P_{dBm} = 10 log_{10}({P_{mW}/{1mW}})$

Power in mW	Power in dBm
0.1 mW	-10 dBm
1 mW	0 dBm
10 mW	10 dBm
100 mW	20 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.

Peak to Average

P1dB

Normally, there is a direct relationship between input and output of an amplifier. As the input increases, the output increases the same amount. However, once the input reaches a certain level, the output signal begins to soft-limit, or compress. A parameter of interest here is the 1 dB compression point. This is the point where the output signal is compressed 1dB from an ideal input/output transfer function. This is shown in the figure within the region where the ideal slope = 1 line becomes dotted, and the actual response exhibits compression (solid).

Typically, the 1 dB compression point is a function of frequency, and as one would expect, the distortion is worse at higher frequencies.

Noise

Distortion

Power Supply Limits

The relationship between dBm (power with respect to 1mW) and Volts peak-peak for a sinusoidal signal in a 50-Ohm systems is:

dBm	mW	Volts_rms	Volts_pp
-10	0.1	70.711 mV	199.970 mV
0	1	223.607 mV	632.360 mV
5	3.16	0.398 V	1.125 V
10	10	0.707 V	2.000 V
15	31.6	1.257 V	3.556 V
20	100	2.236 V	6.324 V

The question is, how do we get +20dBm (6.324V _peak-peak) out of a system, when the power supply is limited to 5V? The trick is in how we connect the output stage. The output stage (RFOUT) is connected to Vcc through the inductor L1. From a DC perspective, inductors become short circuits, and RFOUT is setting at 5.0V, allowing a 10V_peak-peak swing from the amplifier. This is also why it is AC-coupled by the output capacitor before it attaches to the antenna.

Power Dissipation

Supply Current in the ADL5606 datasheet is specified for a max on 390mA at 5.0V (or 1.95W). Although the ADL5606 is packaged in a thermally efficient 4 mm × 4 mm, 16-lead LFCSP (thermal resistance from junction to air (θ_JA) is 52.9°C/W. This 1.95W dissipation times the θ_JA is a temperature increase of 103.2 °C. Given a maximum junction temperature of 150°C, we either only use the part in sub 46.845°C environments, or work harder on spreading the heat out of the package, onto the PCB.

S Parameters

Scattering or 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:

Measurement	Leaving Port	Entering Port
S11	1	1
S12	1	2
S21	2	1
S22	2	2

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.

Depending on what you are measuring - each measurement can be more important than another. For example, for an amplifier, S21 measures the gain of the amplifier, with port 1 being the input and port 2 being the output. If an amplifier's S21=0 dB, the amplifier has a gain of 1. For an antenna, S11 represents how much power is reflected from the antenna back, and hence is known as the reflection coefficient (or return loss). If an antenna's S11=0 dB, then all the power being sent to the antenna is reflected from the antenna and nothing is radiated.

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.

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Table of Contents

Amplifiers

Transmission

Free Space Path Loss