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# Programmable Gain Amplifiers

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Raul

# Overview

# Introduction

# Design and implementation

## PGA with parallel resistor matrix

## PGA with series resistor matrix

# Procedure

# Equipment

In this laboratory, we will get familiarized with the main parameters and typical requirements for amplifiers with controlled gain (variable/programmable gain amplifiers (PGAs).

There are two main types of amplifiers with controlled gain:

- Variable Gain Amplifiers (VGA): amplifiers with the gain value determined by a continous-time signal – an analog voltage or current. As a result the gain can take any value within the gain range of the amplifier.
- Programmable Gain Amplifiers (PGA) – sometimes also called Digitally-Controlled Amplifier: an amplifier whose gain can be modified in steps according to a digital control signal. Note that in this case the amplifier gain can take values only from a pre-defined, finite set of possibilities. In general, the gain value is modified by using switches turned on/off by the digital controls.

Fig1: A simple PGA topology and implementation for the switches

Fig. 1 presents a PGA with constant input resistance. The feedback resistance is implemented using a digitally controlled resistor matrix and the switches are implemented using MOS transistors. A switch present in the signal path introduces a nonlinear resistance – which will degrade the PGA linearity – and parasitic capacitance – that modifies the loop gain characteristic and can decrease the phase margin. The expression of the PGA gain, without taking into account the effect of the switches, is:

The main parameters of a programmable gain amplifier are:

- Minimum amplification
- Maximum amplification
- Gain resolution = the minimum step by which the gain can be controlled
- The bandwidth
- Input resistance
- Linearity
- Current consumption

The CD4051B analog MUX will be supplied with +5V/-5V from the adjustable reference voltages VREF1 and VREF2. The control bits will be set using Switch1 and Switch2 on the Helpkit board.

Fig.2: CD4051B MUX diagram and its pinout

The inverting programmable gain amplifier with parallel resistor matrix is illustrated in Fig. 3. The switches are implemented with the CD4051B analog multiplexer.

Fig. 3. PGA implemented with AO, inverting amplifier structure, parallel connection of resistors that implement equivalent reaction resistance. On the left the electrical diagram in which switches are implemented with MOS transistors and on the right the electrical scheme implemented

Similarly, the inverting programmable gain amplifier with series resistor matrix is illustrated in Fig. 4.

Fig. 4: PGA implemented with AO, inverting amplifier structure, series connection of resistors that implement equivalent reaction resistance. On the left the electrical diagram in which switches are implemented with MOS transistors and on the right the electrical scheme implemented

- Implement the circuit in Fig.3 and measure the low-frequency gain of the implemented amplifier, for each gain stage.
- Set the Hantek generator to generate a harmonic signal (sine) with low-medium amplitude (for example 1V) and low frequency (for example 100Hz). Apply this signal to the input of the PGA.
- Measure the amplitude of the signal at the input and output of the PGA and calculate the gain of the amplifier
- Fill the following table

Table 1 PGA parameters for parallel resistor matrix

SW2 | SW1 | R_{in}[ohm] |
R_{F_ech}[ohm] |
AV_{estimated}[dB] |
AV_{measured}[dB] |

0 | 0 | R_{G}=10k |
R_{F1}=5k |
-6 | |

0 | 1 | R_{G}=10k |
R_{F2}=10k |
0 | |

1 | 0 | R_{G}=10k |
R_{F3}=20k |
6 | |

1 | 1 | R_{G}=10k |
R_{F4}=40k |
12 |

- Implement the circuit in Figure 3 and repeat steps 2,3 and 4 for the following table

Table 2: PGA parameters for series resistor matrix

SW2 | SW1 | R_{in}[ohm] |
R_{F_ech}[ohm] |
AV_{estimated} [dB] |
AV_{measured} [dB] |

0 | 0 | R_{G}=10k |
R_{F1}=5k |
-6 | |

0 | 1 | R_{G}=10k |
R_{F1}+R_{F2}=10k |
0 | |

1 | 0 | R_{G}=10k |
R_{F1}+R_{F2}+R_{F3}=20k |
6 | |

1 | 1 | R_{G}=10k |
R_{F1}+R_{F2}+R_{F3}+R_{F4}=40k |
12 |

- The Home Electronics Laboratory Platform (HELP) board
- Hantek 2D42 Handheld Oscilloscope
- 1x The CD4051B analog MUX
- 1 x TL082 OP-Amp
- 2 x 5kΩ resistors, 2 x 10kΩ resistors, 1 x 20kΩ resistor, 1 x 40kΩ resistor