#### Example 1.5 | #### Question 1.10 | #### In-depth

## The vector modulator

#### The arrangement of mixers and a combiner (summing device) shown here forms an extremely useful building block in digital communications systems. It achieves a linear frequency translation of all components in the input signal (represented by its in-phase and quadrature components) by a carrier frequency component (also represented by its in-phase and quadrature components). This building block is often referred to as a vector modulator or quadrature modulator and, as we shall see, can be used for both frequency up-conversion and down-conversion. |

#### The output of the two mixing processes is given by: #### #### and #### #### which when subtracted from each other result in a single up-converted component: #### #### and when summed give a down-converted component: