# Resonant frequency of circular microstrip antennas with and without air gaps

##### Citations

275 citations

### Cites methods from "Resonant frequency of circular micr..."

...6 GHz using formulas in [12] and the optimum dimension of...

[...]

...Other techniques investigated ground planes with modified shapes like “ ” as in [12]....

[...]

123 citations

### Cites background from "Resonant frequency of circular micr..."

...It can be seen that the E-fields of the excited patch (Patch 1) nearly point to the same direction (the +y-direction) along the E1-edge, but demonstrate a direction reversal along the E2-edge, indicating that the excited Patch 1 operates in the normal TM01 mode [16], [17], [21]....

[...]

...22 GHz, indicating that the cavity operates in the normal TM01 mode [16], [17]....

[...]

114 citations

### Cites methods from "Resonant frequency of circular micr..."

...More accurate results could have been achieved if dynamic was used in the new formula [ 35 ]....

[...]

110 citations

### Cites methods from "Resonant frequency of circular micr..."

...9(a) shows a two element probe-fed array with a single ring CR-DGS and the patch is designed to resonate around 10 GHz using the CAD formulas in [19] and [20]....

[...]

99 citations

### Cites background from "Resonant frequency of circular micr..."

...articles [13], [19], the resonant frequencies of the two CP modes can be expressed as...

[...]

##### References

296 citations

### "Resonant frequency of circular micr..." refers background or methods or result in this paper

...much improved over the earlier ones [ 11 ], [12], [15], [16] and is widely applicable to the entire range of dielectric constants and to all values of the antenna....

[...]

...Watkins [13] was modified by Wolff and Knoppik [ 11 ] incorporating the effect of the fringing fields in a disk capacitor and by introducing dynamic dielectric constant defined through (4)‐(7)....

[...]

...The evaluation of is straightforward, as given by (1), and that of is a function of the static main and static fringing capacitances and the mode of resonance as given by [ 11 ]...

[...]

...The formulation, though incorporating the improved results of some earlier works [ 11 ], [12], is valid for the antenna parameters and . Thus the model [10] is not applicable to small values of , particularly when an air gap increases the value of ( in Fig. 1). Moreover, the calculation of the resonant frequency in [10] involves an erroneous equation, as discussed in the following sections....

[...]

...Following the analytical model by Wolff and Knoppik [ 11 ], an improved formulation is presented by introducing a new effective dielectric constant in place of the dynamic dielectric constant [11, eq. 18] of the medium below the patch to calculate the resonant frequency of a circular microstrip antenna as...

[...]

229 citations

### "Resonant frequency of circular micr..." refers background in this paper

...much improved over the earlier ones [11], [12], [ 15 ], [16] and is widely applicable to the entire range of dielectric constants and to all values of the antenna....

[...]

169 citations

155 citations

### "Resonant frequency of circular micr..." refers methods in this paper

...Watkins [ 13 ] was modified by Wolff and Knoppik [11] incorporating the effect of the fringing fields in a disk capacitor and by introducing dynamic dielectric constant defined through (4)‐(7)....

[...]

121 citations